RFC 9340

Internet Research Task Force (IRTF) W. Kozlowski

Request for Comments: 9340 S. Wehner

Category: Informational QuTech

ISSN: 2070-1721 R. Van Meter

Keio University

B. Rijsman

Individual

A. S. Cacciapuoti

M. Caleffi

University of Naples Federico II

S. Nagayama

Mercari, Inc.

March 2023

# Abstract

The vision of a quantum internet is to enhance existing Internet

technology by enabling quantum communication between any two points

on Earth. To achieve this goal, a quantum network stack should be

built from the ground up to account for the fundamentally new

properties of quantum entanglement. The first quantum entanglement

networks have been realised, but there is no practical proposal for

how to organise, utilise, and manage such networks. In this

document, we attempt to lay down the framework and introduce some

basic architectural principles for a quantum internet. This is

intended for general guidance and general interest. It is also

intended to provide a foundation for discussion between physicists

and network specialists. This document is a product of the Quantum

Internet Research Group (QIRG).

# Status of This Memo

This document is not an Internet Standards Track specification; it is

published for informational purposes.

This document is a product of the Internet Research Task Force

(IRTF). The IRTF publishes the results of Internet-related research

and development activities. These results might not be suitable for

deployment. This RFC represents the consensus of the Quantum

Internet Research Group of the Internet Research Task Force (IRTF).

Documents approved for publication by the IRSG are not candidates for

any level of Internet Standard; see Section 2 of RFC 7841.

Information about the current status of this document, any errata,

and how to provide feedback on it may be obtained at

https://www.rfc-editor.org/info/rfc9340.

# Copyright Notice

Copyright (c) 2023 IETF Trust and the persons identified as the

document authors. All rights reserved.

This document is subject to BCP 78 and the IETF Trust's Legal

Provisions Relating to IETF Documents

(https://trustee.ietf.org/license-info) in effect on the date of

publication of this document. Please review these documents

carefully, as they describe your rights and restrictions with respect

to this document.

# Table of Contents

1. Introduction

2. Quantum Information

2.1. Quantum State

2.2. Qubit

2.3. Multiple Qubits

3. Entanglement as the Fundamental Resource

4. Achieving Quantum Connectivity

4.1. Challenges

4.1.1. The Measurement Problem

4.1.2. No-Cloning Theorem

4.1.3. Fidelity

4.1.4. Inadequacy of Direct Transmission

4.2. Bell Pairs

4.3. Teleportation

4.4. The Life Cycle of Entanglement

4.4.1. Elementary Link Generation

4.4.2. Entanglement Swapping

4.4.3. Error Management

4.4.4. Delivery

5. Architecture of a Quantum Internet

5.1. Challenges

5.2. Classical Communication

5.3. Abstract Model of the Network

5.3.1. The Control Plane and the Data Plane

5.3.2. Elements of a Quantum Network

5.3.3. Putting It All Together

5.4. Physical Constraints

5.4.1. Memory Lifetimes

5.4.2. Rates

5.4.3. Communication Qubits

5.4.4. Homogeneity

6. Architectural Principles

6.1. Goals of a Quantum Internet

6.2. The Principles of a Quantum Internet

7. A Thought Experiment Inspired by Classical Networks

8. Security Considerations

9. IANA Considerations

10. Informative References

Acknowledgements

# Authors' Addresses

# 1. Introduction

Quantum networks are distributed systems of quantum devices that

utilise fundamental quantum mechanical phenomena such as

superposition, entanglement, and quantum measurement to achieve

capabilities beyond what is possible with non-quantum (classical)

networks [Kimble08]. Depending on the stage of a quantum network

[Wehner18], such devices may range from simple photonic devices

capable of preparing and measuring only one quantum bit (qubit) at a

time all the way to large-scale quantum computers of the future. A

quantum network is not meant to replace classical networks but rather

to form an overall hybrid classical-quantum network supporting new

capabilities that are otherwise impossible to realise [VanMeterBook].

For example, the most well-known application of quantum

communication, Quantum Key Distribution (QKD) [QKD], can create and

distribute a pair of symmetric encryption keys in such a way that the

security of the entire process relies on the laws of physics (and

thus can be mathematically proven to be unbreakable) rather than the

intractability of certain mathematical problems [Bennett14]

[Ekert91]. Small networks capable of QKD have even already been

deployed at short (roughly 100-kilometre) distances [Elliott03]

[Peev09] [Aguado19] [Joshi20].

The quantum networking paradigm also offers promise for a range of

new applications beyond quantum cryptography, such as distributed

quantum computation [Cirac99] [Crepeau02]; secure quantum computing

in the cloud [Fitzsimons17]; quantum-enhanced measurement networks

[Giovannetti04]; or higher-precision, long-baseline telescopes

[Gottesman12]. These applications are much more demanding than QKD,

and networks capable of executing them are in their infancy. The

first fully quantum, multinode network capable of sending, receiving,

and manipulating distributed quantum information has only recently

been realised [Pompili21.1].

Whilst a lot of effort has gone into physically realising and

connecting such devices, and making improvements to their speed and

error tolerance, no proposals for how to run these networks have been

worked out at the time of this writing. To draw an analogy with a

classical network, we are at a stage where we can start to physically

connect our devices and send data, but all sending, receiving, buffer

management, connection synchronisation, and so on must be managed by

the application directly by using low-level, custom-built, and

hardware-specific interfaces, rather than being managed by a network

stack that exposes a convenient high-level interface, such as

sockets. Only recently was the first-ever attempt at such a network

stack experimentally demonstrated in a laboratory setting

[Pompili21.2]. Furthermore, whilst physical mechanisms for

transmitting quantum information exist, there are no robust protocols

for managing such transmissions.

This document, produced by the Quantum Internet Research Group

(QIRG), introduces quantum networks and presents general guidelines

for the design and construction of such networks. Overall, it is

intended as an introduction to the subject for network engineers and

researchers. It should not be considered as a conclusive statement

on how quantum networks should or will be implemented. This document

was discussed on the QIRG mailing list and several IETF meetings. It

represents the consensus of the QIRG members, of both experts in the

subject matter (from the quantum and networking domains) and

newcomers who are the target audience.

# 2. Quantum Information

In order to understand the framework for quantum networking, a basic

understanding of quantum information theory is necessary. The

following sections aim to introduce the minimum amount of knowledge

necessary to understand the principles of operation of a quantum

network. This exposition was written with a classical networking

audience in mind. It is assumed that the reader has never before

been exposed to any quantum physics. We refer the reader to

[SutorBook] and [NielsenChuang] for an in-depth introduction to

quantum information systems.

## 2.1. Quantum State

A quantum mechanical system is described by its quantum state. A

quantum state is an abstract object that provides a complete

description of the system at that particular moment. When combined

with the rules of the system's evolution in time, such as a quantum

circuit, it also then provides a complete description of the system

at all times. For the purposes of computing and networking, the

classical equivalent of a quantum state would be a string or stream

of logical bit values. These bits provide a complete description of

what values we can read out from that string at that particular

moment, and when combined with its rules for evolution in time, such

as a logical circuit, we will also know its value at any other time.

Just like a single classical bit, a quantum mechanical system can be

simple and consist of a single particle, e.g., an atom or a photon of

light. In this case, the quantum state provides the complete

description of that one particle. Similarly, just like a string of

bits consists of multiple bits, a single quantum state can be used to

also describe an ensemble of many particles. However, because

quantum states are governed by the laws of quantum mechanics, their

behaviour is significantly different to that of a string of bits. In

this section, we will summarise the key concepts to understand these

differences. We will then explain their consequences for networking

in the rest of this document.

## 2.2. Qubit

The differences between quantum computation and classical computation

begin at the bit level. A classical computer operates on the binary

alphabet { 0, 1 }. A quantum bit, called a qubit, exists over the

same binary space, but unlike the classical bit, its state can exist

in a superposition of the two possibilities:

|qubit⟩ = a |0⟩ + b |1⟩,

where |X⟩ is Dirac's ket notation for a quantum state (the value that

a qubit holds) -- here, the binary 0 and 1 -- and the coefficients a

and b are complex numbers called probability amplitudes. Physically,

such a state can be realised using a variety of different

technologies such as electron spin, photon polarisation, atomic

energy levels, and so on.

Upon measurement, the qubit loses its superposition and irreversibly

collapses into one of the two basis states, either |0⟩ or |1⟩. Which

of the two states it ends up in may not be deterministic but can be

determined from the readout of the measurement. The measurement

result is a classical bit, 0 or 1, corresponding to |0⟩ and |1⟩,

respectively. The probability of measuring the state in the |0⟩

state is |a|^2; similarly, the probability of measuring the state in

the |1⟩ state is |b|^2, where |a|^2 + |b|^2 = 1. This randomness is

not due to our ignorance of the underlying mechanisms but rather is a

fundamental feature of a quantum mechanical system [Aspect81].

The superposition property plays an important role in fundamental

gate operations on qubits. Since a qubit can exist in a

superposition of its basis states, the elementary quantum gates are

able to act on all states of the superposition at the same time. For

example, consider the NOT gate:

NOT (a |0⟩ + b |1⟩) → a |1⟩ + b |0⟩.

It is important to note that "qubit" can have two meanings. In the

first meaning, "qubit" refers to a physical quantum *system* whose

quantum state can be expressed as a superposition of two basis

states, which we often label |0⟩ and |1⟩. Here, "qubit" refers to a

physical implementation akin to what a flip-flop, switch, voltage, or

current would be for a classical bit. In the second meaning, "qubit"

refers to the abstract quantum *state* of a quantum system with such

two basis states. In this case, the meaning of "qubit" is akin to

the logical value of a bit, from classical computing, i.e., "logical

0" or "logical 1". The two concepts are related, because a physical

"qubit" (first meaning) can be used to store the abstract "qubit"

(second meaning). Both meanings are used interchangeably in

literature, and the meaning is generally clear from the context.

## 2.3. Multiple Qubits

When multiple qubits are combined in a single quantum state, the

space of possible states grows exponentially and all these states can

coexist in a superposition. For example, the general form of a two-

qubit register is

a |00⟩ + b |01⟩ + c |10⟩ + d |11⟩,

where the coefficients have the same probability amplitude

interpretation as for the single-qubit state. Each state represents

a possible outcome of a measurement of the two-qubit register. For

example, |01⟩ denotes a state in which the first qubit is in the

state |0⟩ and the second is in the state |1⟩.

Performing single-qubit gates affects the relevant qubit in each of

the superposition states. Similarly, two-qubit gates also act on all

the relevant superposition states, but their outcome is far more

interesting.

Consider a two-qubit register where the first qubit is in the

superposed state (|0⟩ + |1⟩)/sqrt(2) and the other is in the

state |0⟩. This combined state can be written as

(|0⟩ + |1⟩)/sqrt(2) x |0⟩ = (|00⟩ + |10⟩)/sqrt(2),

where x denotes a tensor product (the mathematical mechanism for

combining quantum states together).

The constant 1/sqrt(2) is called the normalisation factor and

reflects the fact that the probabilities of measuring either a |0⟩ or

a |1⟩ for the first qubit add up to one.

Let us now consider the two-qubit Controlled NOT, or CNOT, gate. The

CNOT gate takes as input two qubits -- a control and a target -- and

applies the NOT gate to the target if the control qubit is set. The

truth table looks like

+====+=====+

| IN | OUT |

+====+=====+

| 00 | 00 |

+----+-----+

| 01 | 01 |

+----+-----+

| 10 | 11 |

+----+-----+

| 11 | 10 |

+----+-----+

Table 1: CNOT Truth Table

Now, consider performing a CNOT gate on the state with the first

qubit being the control. We apply a two-qubit gate on all the

superposition states:

CNOT (|00⟩ + |10⟩)/sqrt(2) → (|00⟩ + |11⟩)/sqrt(2).

What is so interesting about this two-qubit gate operation? The

final state is *entangled*. There is no possible way of representing

that quantum state as a product of two individual qubits; they are no

longer independent. That is, it is not possible to describe the

quantum state of either of the individual qubits in a way that is

independent of the other qubit. Only the quantum state of the system

that consists of both qubits provides a physically complete

description of the two-qubit system. The states of the two

individual qubits are now correlated beyond what is possible to

achieve classically. Neither qubit is in a definite |0⟩ or |1⟩

state, but if we perform a measurement on either one, the outcome of

the partner qubit will *always* yield the exact same outcome. The

final state, whether it's |00⟩ or |11⟩, is fundamentally random as

before, but the states of the two qubits following a measurement will

always be identical. One can think of this as flipping two coins,

but both coins always land on "heads" or both land on "tails"

together -- something that we know is impossible classically.

Once a measurement is performed, the two qubits are once again

independent. The final state is either |00⟩ or |11⟩, and both of

these states can be trivially decomposed into a product of two

individual qubits. The entanglement has been consumed, and the

entangled state must be prepared again.

# 3. Entanglement as the Fundamental Resource

Entanglement is the fundamental building block of quantum networks.

Consider the state from the previous section:

(|00⟩ + |11⟩)/sqrt(2).

Neither of the two qubits is in a definite |0⟩ or |1⟩ state, and we

need to know the state of the entire register to be able to fully

describe the behaviour of the two qubits.

Entangled qubits have interesting non-local properties. Consider

sending one of the qubits to another device. This device could in

principle be anywhere: on the other side of the room, in a different

country, or even on a different planet. Provided negligible noise

has been introduced, the two qubits will forever remain in the

entangled state until a measurement is performed. The physical

distance does not matter at all for entanglement.

This lies at the heart of quantum networking, because it is possible

to leverage the non-classical correlations provided by entanglement

in order to design completely new types of application protocols that

are not possible to achieve with just classical communication.

Examples of such applications are quantum cryptography [Bennett14]

[Ekert91], blind quantum computation [Fitzsimons17], or distributed

quantum computation [Crepeau02].

Entanglement has two very special features from which one can derive

some intuition about the types of applications enabled by a quantum

network.

The first stems from the fact that entanglement enables stronger-

than-classical correlations, leading to opportunities for tasks that

require coordination. As a trivial example, consider the problem of

consensus between two nodes who want to agree on the value of a

single bit. They can use the quantum network to prepare the state

(|00⟩ + |11⟩)/sqrt(2) with each node holding one of the two qubits.

Once either of the two nodes performs a measurement, the state of the

two qubits collapses to either |00⟩ or |11⟩, so whilst the outcome is

random and does not exist before measurement, the two nodes will

always measure the same value. We can also build the more general

multi-qubit state (|00...⟩ + |11...⟩)/sqrt(2) and perform the same

algorithm between an arbitrary number of nodes. These stronger-than-

classical correlations generalise to measurement schemes that are

more complicated as well.

The second feature of entanglement is that it cannot be shared, in

the sense that if two qubits are maximally entangled with each other,

then it is physically impossible for these two qubits to also be

entangled with a third qubit [Terhal04]. Hence, entanglement forms a

sort of private and inherently untappable connection between two

nodes once established.

Entanglement is created through local interactions between two qubits

or as a product of the way the qubits were created (e.g., entangled

photon pairs). To create a distributed entangled state, one can then

physically send one of the qubits to a remote node. It is also

possible to directly entangle qubits that are physically separated,

but this still requires local interactions between some other qubits

that the separated qubits are initially entangled with. Therefore,

it is the transmission of qubits that draws the line between a

genuine quantum network and a collection of quantum computers

connected over a classical network.

A quantum network is defined as a collection of nodes that is able to

exchange qubits and distribute entangled states amongst themselves.

A quantum node that is able only to communicate classically with

another quantum node is not a member of a quantum network.

Services and applications that are more complex can be built on top

of entangled states distributed by the network; for example, see

[ZOO].

# 4. Achieving Quantum Connectivity

This section explains the meaning of quantum connectivity and the

necessary physical processes at an abstract level.

## 4.1. Challenges

A quantum network cannot be built by simply extrapolating all the

classical models to their quantum analogues. Sending qubits over a

wire like we send classical bits is simply not as easy to do. There

are several technological as well as fundamental challenges that make

classical approaches unsuitable in a quantum context.

### 4.1.1. The Measurement Problem

In classical computers and networks, we can read out the bits stored

in memory at any time. This is helpful for a variety of purposes

such as copying, error detection and correction, and so on. This is

not possible with qubits.

A measurement of a qubit's state will destroy its superposition and

with it any entanglement it may have been part of. Once a qubit is

being processed, it cannot be read out until a suitable point in the

computation, determined by the protocol handling the qubit, has been

reached. Therefore, we cannot use the same methods known from

classical computing for the purposes of error detection and

correction. Nevertheless, quantum error detection and correction

schemes exist that take this problem into account, and how a network

chooses to manage errors will have an impact on its architecture.

### 4.1.2. No-Cloning Theorem

Since directly reading the state of a qubit is not possible, one

could ask if we can simply copy a qubit without looking at it.

Unfortunately, this is fundamentally not possible in quantum

mechanics [Park70] [Wootters82].

The no-cloning theorem states that it is impossible to create an

identical copy of an arbitrary, unknown quantum state. Therefore, it

is also impossible to use the same mechanisms that worked for

classical networks for signal amplification, retransmission, and so

on, as they all rely on the ability to copy the underlying data.

Since any physical channel will always be lossy, connecting nodes

within a quantum network is a challenging endeavour, and its

architecture must at its core address this very issue.

### 4.1.3. Fidelity

In general, it is expected that a classical packet arrives at its

destination without any errors introduced by hardware noise along the

way. This is verified at various levels through a variety of error

detection and correction mechanisms. Since we cannot read or copy a

quantum state, error detection and correction are more involved.

To describe the quality of a quantum state, a physical quantity

called fidelity is used [NielsenChuang]. Fidelity takes a value

between 0 and 1 -- higher is better, and less than 0.5 means the

state is unusable. It measures how close a quantum state is to the

state we have tried to create. It expresses the probability that the

state will behave exactly the same as our desired state. Fidelity is

an important property of a quantum system that allows us to quantify

how much a particular state has been affected by noise from various

sources (gate errors, channel losses, environment noise).

Interestingly, quantum applications do not need perfect fidelity to

be able to execute -- as long as the fidelity is above some

application-specific threshold, they will simply operate at lower

rates. Therefore, rather than trying to ensure that we always

deliver perfect states (a technologically challenging task),

applications will specify a minimum threshold for the fidelity, and

the network will try its best to deliver it. A higher fidelity can

be achieved by either having hardware produce states of better

fidelity (sometimes one can sacrifice rate for higher fidelity) or

employing quantum error detection and correction mechanisms (see

[Mural16] and Chapter 11 of [VanMeterBook]).

### 4.1.4. Inadequacy of Direct Transmission

Conceptually, the most straightforward way to distribute an entangled

state is to simply transmit one of the qubits directly to the other

end across a series of nodes while performing sufficient forward

Quantum Error Correction (QEC) (Section 4.4.3.2) to bring losses down

to an acceptable level. Despite the no-cloning theorem and the

inability to directly measure a quantum state, error-correcting

mechanisms for quantum communication exist [Jiang09] [Fowler10]

[Devitt13] [Mural16]. However, QEC makes very high demands on both

resources (physical qubits needed) and their initial fidelity.

Implementation is very challenging, and QEC is not expected to be

used until later generations of quantum networks are possible (see

Figure 2 of [Mural16] and Section 4.4.3.3 of this document). Until

then, quantum networks rely on entanglement swapping (Section 4.4.2)

and teleportation (Section 4.3). This alternative relies on the

observation that we do not need to be able to distribute any

arbitrary entangled quantum state. We only need to be able to

distribute any one of what are known as the Bell pair states

[Briegel98].

## 4.2. Bell Pairs

Bell pair states are the entangled two-qubit states:

|00⟩ + |11⟩,

|00⟩ - |11⟩,

|01⟩ + |10⟩,

|01⟩ - |10⟩,

where the constant 1/sqrt(2) normalisation factor has been ignored

for clarity. Any of the four Bell pair states above will do, as it

is possible to transform any Bell pair into another Bell pair with

local operations performed on only one of the qubits. When each

qubit in a Bell pair is held by a separate node, either node can

apply a series of single-qubit gates to their qubit alone in order to

transform the state between the different variants.

Distributing a Bell pair between two nodes is much easier than

transmitting an arbitrary quantum state over a network. Since the

state is known, handling errors becomes easier, and small-scale error

correction (such as entanglement distillation, as discussed in

Section 4.4.3.1), combined with reattempts, becomes a valid strategy.

The reason for using Bell pairs specifically as opposed to any other

two-qubit state is that they are the maximally entangled two-qubit

set of basis states. Maximal entanglement means that these states

have the strongest non-classical correlations of all possible two-

qubit states. Furthermore, since single-qubit local operations can

never increase entanglement, states that are less entangled would

impose some constraints on distributed quantum algorithms. This

makes Bell pairs particularly useful as a generic building block for

distributed quantum applications.

## 4.3. Teleportation

The observation that we only need to be able to distribute Bell pairs

relies on the fact that this enables the distribution of any other

arbitrary entangled state. This can be achieved via quantum state

teleportation [Bennett93]. Quantum state teleportation consumes an

unknown qubit state that we want to transmit and recreates it at the

desired destination. This does not violate the no-cloning theorem,

as the original state is destroyed in the process.

To achieve this, an entangled pair needs to be distributed between

the source and destination before teleportation commences. The

source then entangles the transmission qubit with its end of the pair

and performs a readout of the two qubits (the sum of these operations

is called a Bell state measurement). This consumes the Bell pair's

entanglement, turning the source and destination qubits into

independent states. The measurement yields two classical bits, which

the source sends to the destination over a classical channel. Based

on the value of the received two classical bits, the destination

performs one of four possible corrections (called the Pauli

corrections) on its end of the pair, which turns it into the unknown

qubit state that we wanted to transmit. This requirement to

communicate the measurement readout over a classical channel

unfortunately means that entanglement cannot be used to transmit

information faster than the speed of light.

The unknown quantum state that was transmitted was never fed into the

network itself. Therefore, the network needs to only be able to

reliably produce Bell pairs between any two nodes in the network.

Thus, a key difference between a classical data plane and a quantum

data plane is that a classical data plane carries user data but a

quantum data plane provides the resources for the user to transmit

user data themselves without further involvement of the network.

## 4.4. The Life Cycle of Entanglement

Reducing the problem of quantum connectivity to one of generating a

Bell pair has reduced the problem to a simpler, more fundamental

case, but it has not solved it. In this section, we discuss how

these entangled pairs are generated in the first place and how their

two qubits are delivered to the end-points.

### 4.4.1. Elementary Link Generation

In a quantum network, entanglement is always first generated locally

(at a node or an auxiliary element), followed by a movement of one or

both of the entangled qubits across the link through quantum

channels. In this context, photons (particles of light) are the

natural candidate for entanglement carriers. Because these photons

carry quantum states from place to place at high speed, we call them

flying qubits. The rationale for this choice is related to the

advantages provided by photons, such as moderate interaction with the

environment leading to moderate decoherence; convenient control with

standard optical components; and high-speed, low-loss transmissions.

However, since photons are hard to store, a transducer must transfer

the flying qubit's state to a qubit suitable for information

processing and/or storage (often referred to as a matter qubit).

Since this process may fail, in order to generate and store

entanglement efficiently, we must be able to distinguish successful

attempts from failures. Entanglement generation schemes that are

able to announce successful generation are called heralded

entanglement generation schemes.

There exist three basic schemes for heralded entanglement generation

on a link through coordinated action of the two nodes at the two ends

of the link [Cacciapuoti19]:

"At mid-point": In this scheme, an entangled photon pair source

sitting midway between the two nodes with matter qubits sends an

entangled photon through a quantum channel to each of the nodes.

There, transducers are invoked to transfer the entanglement from

the flying qubits to the matter qubits. In this scheme, the

transducers know if the transfers succeeded and are able to herald

successful entanglement generation via a message exchange over the

classical channel.

"At source": In this scheme, one of the two nodes sends a flying

qubit that is entangled with one of its matter qubits. A

transducer at the other end of the link will transfer the

entanglement from the flying qubit to one of its matter qubits.

Just like in the previous scheme, the transducer knows if its

transfer succeeded and is able to herald successful entanglement

generation with a classical message sent to the other node.

"At both end-points": In this scheme, both nodes send a flying qubit

that is entangled with one of their matter qubits. A detector

somewhere in between the nodes performs a joint measurement on the

flying qubits, which stochastically projects the remote matter

qubits into an entangled quantum state. The detector knows if the

entanglement succeeded and is able to herald successful

entanglement generation by sending a message to each node over the

classical channel.

The "mid-point source" scheme is more robust to photon loss, but in

the other schemes, the nodes retain greater control over the

entangled pair generation.

Note that whilst photons travel in a particular direction through the

quantum channel the resulting entangled pair of qubits does not have

a direction associated with it. Physically, there is no upstream or

downstream end of the pair.

### 4.4.2. Entanglement Swapping

The problem with generating entangled pairs directly across a link is

that efficiency decreases with channel length. Beyond a few tens of

kilometres in optical fibre or 1000 kilometres in free space (via

satellite), the rate is effectively zero, and due to the no-cloning

theorem we cannot simply amplify the signal. The solution is

entanglement swapping [Briegel98].

A Bell pair between any two nodes in the network can be constructed

by combining the pairs generated along each individual link on a path

between the two end-points. Each node along the path can consume the

two pairs on the two links to which it is connected, in order to

produce a new entangled pair between the two remote ends. This

process is known as entanglement swapping. It can be represented

pictorially as follows:

+---------+ +---------+ +---------+

| A | | B | | C |

| |------| |------| |

| X1~~~~~~~~~~X2 Y1~~~~~~~~~~Y2 |

+---------+ +---------+ +---------+

where X1 and X2 are the qubits of the entangled pair X and Y1 and Y2

are the qubits of entangled pair Y. The entanglement is denoted with

~~. In the diagram above, nodes A and B share the pair X and nodes B

and C share the pair Y, but we want entanglement between A and C.

To achieve this goal, we simply teleport the qubit X2 using the pair

Y. This requires node B to perform a Bell state measurement on the

qubits X2 and Y1 that results in the destruction of the entanglement

between Y1 and Y2. However, X2 is recreated in Y2's place, carrying

with it its entanglement with X1. The end result is shown below:

+---------+ +---------+ +---------+

| A | | B | | C |

| |------| |------| |

| X1~~~~~~~~~~~~~~~~~~~~~~~~~~~X2 |

+---------+ +---------+ +---------+

Depending on the needs of the network and/or application, a final

Pauli correction at the recipient node may not be necessary, since

the result of this operation is also a Bell pair. However, the two

classical bits that form the readout from the measurement at node B

must still be communicated, because they carry information about

which of the four Bell pairs was actually produced. If a correction

is not performed, the recipient must be informed which Bell pair was

received.

This process of teleporting Bell pairs using other entangled pairs is

called entanglement swapping. Quantum nodes that create long-

distance entangled pairs via entanglement swapping are called quantum

repeaters in academic literature [Briegel98]. We will use the same

terminology in this document.

### 4.4.3. Error Management

#### 4.4.3.1. Distillation

Neither the generation of Bell pairs nor the swapping operations are

noiseless operations. Therefore, with each link and each swap, the

fidelity of the state degrades. However, it is possible to create

higher-fidelity Bell pair states from two or more lower-fidelity

pairs through a process called distillation (sometimes also referred

to as purification) [Dur07].

To distil a quantum state, a second (and sometimes third) quantum

state is used as a "test tool" to test a proposition about the first

state, e.g., "the parity of the two qubits in the first state is

even." When the test succeeds, confidence in the state is improved,

and thus the fidelity is improved. The test tool states are

destroyed in the process, so resource demands increase substantially

when distillation is used. When the test fails, the tested state

must also be discarded. Distillation makes low demands on fidelity

and resources compared to QEC, but distributed protocols incur round-

trip delays due to classical communication [Bennett96].

#### 4.4.3.2. Quantum Error Correction (QEC)

Just like classical error correction, QEC encodes logical qubits

using several physical (raw) qubits to protect them from the errors

described in Section 4.1.3 [Jiang09] [Fowler10] [Devitt13] [Mural16].

Furthermore, similarly to its classical counterpart, QEC can not only

correct state errors but also account for lost qubits. Additionally,

if all physical qubits that encode a logical qubit are located at the

same node, the correction procedure can be executed locally, even if

the logical qubit is entangled with remote qubits.

Although QEC was originally a scheme proposed to protect a qubit from

noise, QEC can also be applied to entanglement distillation. Such

QEC-applied distillation is cost effective but requires a higher base

fidelity.

#### 4.4.3.3. Error Management Schemes

Quantum networks have been categorised into three "generations" based

on the error management scheme they employ [Mural16]. Note that

these "generations" are more like categories; they do not necessarily

imply a time progression and do not obsolete each other, though the

later generations do require technologies that are more advanced.

Which generation is used depends on the hardware platform and network

design choices.

Table 2 summarises the generations.

+===========+================+=======================+=============+

| | First | Second generation | Third |

| | generation | | generation |

+===========+================+=======================+=============+

| Loss | Heralded | Heralded entanglement | QEC (no |

| tolerance | entanglement | generation | classical |

| | generation | (bidirectional | signalling) |

| | (bidirectional | classical signalling) | |

| | classical | | |

| | signalling) | | |

+-----------+----------------+-----------------------+-------------+

+-----------+----------------+-----------------------+-------------+

| Error | Entanglement | Entanglement | QEC (no |

| tolerance | distillation | distillation | classical |

| | (bidirectional | (unidirectional | signalling) |

| | classical | classical signalling) | |

| | signalling) | or QEC (no classical | |

| | | signalling) | |

+-----------+----------------+-----------------------+-------------+

Table 2: Classical Signalling and Generations

Generations are defined by the directions of classical signalling

required in their distributed protocols for loss tolerance and error

tolerance. Classical signalling carries the classical bits,

incurring round-trip delays. As described in Section 4.4.3.1, these

delays affect the performance of quantum networks, especially as the

distance between the communicating nodes increases.

Loss tolerance is about tolerating qubit transmission losses between

nodes. Heralded entanglement generation, as described in

Section 4.4.1, confirms the receipt of an entangled qubit using a

heralding signal. A pair of directly connected quantum nodes

repeatedly attempt to generate an entangled pair until the heralding

signal is received. As described in Section 4.4.3.2, QEC can be

applied to complement lost qubits, eliminating the need for

reattempts. Furthermore, since the correction procedure is composed

of local operations, it does not require a heralding signal.

However, it is possible only when the photon loss rate from

transmission to measurement is less than 50%.

Error tolerance is about tolerating quantum state errors.

Entanglement distillation is the easiest mechanism to implement for

improved error tolerance, but it incurs round-trip delays due to the

requirement for bidirectional classical signalling. The alternative,

QEC, is able to correct state errors locally so that it does not need

any classical signalling between the quantum nodes. In between these

two extremes, there is also QEC-applied distillation, which requires

unidirectional classical signalling.

The three "generations" summarised:

1. First-generation quantum networks use heralding for loss

tolerance and entanglement distillation for error tolerance.

These networks can be implemented even with a limited set of

available quantum gates.

2. Second-generation quantum networks improve upon the first

generation with QEC codes for error tolerance (but not loss

tolerance). At first, QEC will be applied to entanglement

distillation only, which requires unidirectional classical

signalling. Later, QEC codes will be used to create logical Bell

pairs that no longer require any classical signalling for the

purposes of error tolerance. Heralding is still used to

compensate for transmission losses.

3. Third-generation quantum networks directly transmit QEC-encoded

qubits to adjacent nodes, as discussed in Section 4.1.4.

Elementary link Bell pairs can now be created without heralding

or any other classical signalling. Furthermore, this also

enables direct transmission architectures in which qubits are

forwarded end to end like classical packets rather than relying

on Bell pairs and entanglement swapping.

Despite the fact that there are important distinctions in how errors

will be managed in the different generations, it is unlikely that all

quantum networks will consistently use the same method. This is due

to different hardware requirements of the different generations and

the practical reality of network upgrades. Therefore, it is

unavoidable that eventually boundaries between different error

management schemes start forming. This will affect the content and

semantics of messages that must cross those boundaries -- for both

connection setup and real-time operation [Nagayama16].

### 4.4.4. Delivery

Eventually, the Bell pairs must be delivered to an application (or

higher-layer protocol) at the two end nodes. A detailed list of such

requirements is beyond the scope of this document. At minimum, the

end nodes require information to map a particular Bell pair to the

qubit in their local memory that is part of this entangled pair.

# 5. Architecture of a Quantum Internet

It is evident from the previous sections that the fundamental service

provided by a quantum network significantly differs from that of a

classical network. Therefore, it is not surprising that the

architecture of a quantum internet will itself be very different from

that of the classical Internet.

## 5.1. Challenges

This subsection covers the major fundamental challenges involved in

building quantum networks. Here, we only describe the fundamental

differences. Technological limitations are described in Section 5.4.

1. Bell pairs are not equivalent to packets that carry payload.

In most classical networks, including Ethernet, Internet Protocol

(IP), and Multi-Protocol Label Switching (MPLS) networks, user

data is grouped into packets. In addition to the user data, each

packet also contains a series of headers that contain the control

information that lets routers and switches forward it towards its

destination. Packets are the fundamental unit in a classical

network.

In a quantum network, the entangled pairs of qubits are the basic

unit of networking. These qubits themselves do not carry any

headers. Therefore, quantum networks will have to send all

control information via separate classical channels, which the

repeaters will have to correlate with the qubits stored in their

memory. Furthermore, unlike a classical packet, which is located

at a single node, a Bell pair consists of two qubits distributed

across two nodes. This has a fundamental impact on how quantum

networks will be managed and how protocols need to be designed.

To make long-distance Bell pairs, the nodes may have to keep

their qubits in their quantum memories and wait until control

information is exchanged before proceeding with the next

operation. This signalling will result in additional latency,

which will depend on the distance between the nodes holding the

two ends of the Bell pair. Error management, such as

entanglement distillation, is a typical example of such control

information exchange [Nagayama21] (see also Section 4.4.3.3).

2. "Store and forward" and "store and swap" quantum networks require

different state management techniques.

As described in Section 4.4.1, quantum links provide Bell pairs

that are undirected network resources, in contrast to directed

frames of classical networks. This phenomenological distinction

leads to architectural differences between quantum networks and

classical networks. Quantum networks combine multiple elementary

link Bell pairs together to create one end-to-end Bell pair,

whereas classical networks deliver messages from one end to the

other end hop by hop.

Classical networks receive data on one interface, store it in

local buffers, and then forward the data to another appropriate

interface. Quantum networks store Bell pairs and then execute

entanglement swapping instead of forwarding in the data plane.

Such quantum networks are "store and swap" networks. In "store

and swap" networks, we do not need to care about the order in

which the Bell pairs were generated, since they are undirected.

However, whilst the ordering does not matter, it is very

important that the right entangled pairs get swapped, and that

the intermediate measurement outcomes (see Section 4.4.2) are

signalled to and correlated with the correct qubits at the other

nodes. Otherwise, the final end-to-end entangled pair will not

be created between the expected end-points or will be in a

different quantum state than expected. For example, rather than

Alice receiving a qubit that is entangled with Bob's qubit, her

qubit is entangled with Charlie's qubit. This distinction makes

control algorithms and optimisation of quantum networks different

from those for classical networks, in the sense that swapping is

stateful in contrast to stateless packet-by-packet forwarding.

Note that, as described in Section 4.4.3.3, third-generation

quantum networks will be able to support a "store and forward"

architecture in addition to "store and swap".

3. An entangled pair is only useful if the locations of both qubits

are known.

A classical network packet logically exists only at one location

at any point in time. If a packet is modified in some way,

whether headers or payload, this information does not need to be

conveyed to anybody else in the network. The packet can be

simply forwarded as before.

In contrast, entanglement is a phenomenon in which two or more

qubits exist in a physically distributed state. Operations on

one of the qubits change the mutual state of the pair. Since the

owner of a particular qubit cannot just read out its state, it

must coordinate all its actions with the owner of the pair's

other qubit. Therefore, the owner of any qubit that is part of

an entangled pair must know the location of its counterpart.

Location, in this context, need not be the explicit spatial

location. A relevant pair identifier, a means of communication

between the pair owners, and an association between the pair ID

and the individual qubits will be sufficient.

4. Generating entanglement requires temporary state.

Packet forwarding in a classical network is largely a stateless

operation. When a packet is received, the router does a lookup

in its forwarding table and sends the packet out of the

appropriate output. There is no need to keep any memory of the

packet any more.

A quantum node must be able to make decisions about qubits that

it receives and is holding in its memory. Since qubits do not

carry headers, the receipt of an entangled pair conveys no

control information based on which the repeater can make a

decision. The relevant control information will arrive

separately over a classical channel. This implies that a

repeater must store temporary state, as the control information

and the qubit it pertains to will, in general, not arrive at the

same time.

## 5.2. Classical Communication

In this document, we have already covered two different roles that

classical communication must perform the following:

* Communicate classical bits of information as part of distributed

protocols such as entanglement swapping and teleportation.

* Communicate control information within a network, including

background protocols such as routing, as well as signalling

protocols to set up end-to-end entanglement generation.

Classical communication is a crucial building block of any quantum

network. All nodes in a quantum network are assumed to have

classical connectivity with each other (within typical administrative

domain limits). Therefore, quantum nodes will need to manage two

data planes in parallel: a classical data plane and a quantum data

plane. Additionally, a node must be able to correlate information

between the two planes so that the control information received on a

classical channel can be applied to the qubits managed by the quantum

data plane.

## 5.3. Abstract Model of the Network

### 5.3.1. The Control Plane and the Data Plane

Control plane protocols for quantum networks will have many

responsibilities similar to their classical counterparts, namely

discovering the network topology, resource management, populating

data plane tables, etc. Most of these protocols do not require the

manipulation of quantum data and can operate simply by exchanging

classical messages only. There may also be some control plane

functionality that does require the handling of quantum data

[QI-Scenarios]. As it is not clear if there is much benefit in

defining a separate quantum control plane given the significant

overlap in responsibilities with its classical counterpart, the

question of whether there should be a separate quantum control plane

is beyond the scope of this document.

However, the data plane separation is much more distinct, and there

will be two data planes: a classical data plane and a quantum data

plane. The classical data plane processes and forwards classical

packets. The quantum data plane processes and swaps entangled pairs.

Third-generation quantum networks may also forward qubits in addition

to swapping Bell pairs.

In addition to control plane messages, there will also be control

information messages that operate at the granularity of individual

entangled pairs, such as heralding messages used for elementary link

generation (Section 4.4.1). In terms of functionality, these

messages are closer to classical packet headers than control plane

messages, and thus we consider them to be part of the quantum data

plane. Therefore, a quantum data plane also includes the exchange of

classical control information at the granularity of individual qubits

and entangled pairs.

### 5.3.2. Elements of a Quantum Network

We have identified quantum repeaters as the core building block of a

quantum network. However, a quantum repeater will have to do more

than just entanglement swapping in a functional quantum network. Its

key responsibilities will include the following:

1. Creating link-local entanglement between neighbouring nodes.

2. Extending entanglement from link-local pairs to long-range pairs

through entanglement swapping.

3. Performing distillation to manage the fidelity of the produced

pairs.

4. Participating in the management of the network (routing, etc.).

Not all quantum repeaters in the network will be the same; here, we

break them down further:

Quantum routers (controllable quantum nodes): A quantum router is a

quantum repeater with a control plane that participates in the

management of the network and will make decisions about which

qubits to swap to generate the requested end-to-end pairs.

Automated quantum nodes: An automated quantum node is a data-plane-

only quantum repeater that does not participate in the network

control plane. Since the no-cloning theorem precludes the use of

amplification, long-range links will be established by chaining

multiple such automated nodes together.

End nodes: End nodes in a quantum network must be able to receive

and handle an entangled pair, but they do not need to be able to

perform an entanglement swap (and thus are not necessarily quantum

repeaters). End nodes are also not required to have any quantum

memory, as certain quantum applications can be realised by having

the end node measure its qubit as soon as it is received.

Non-quantum nodes: Not all nodes in a quantum network need to have a

quantum data plane. A non-quantum node is any device that can

handle classical network traffic.

Additionally, we need to identify two kinds of links that will be

used in a quantum network:

Quantum links: A quantum link is a link that can be used to generate

an entangled pair between two directly connected quantum

repeaters. This may include additional mid-point elements as

described in Section 4.4.1. It may also include a dedicated

classical channel that is to be used solely for the purpose of

coordinating the entanglement generation on this quantum link.

Classical links: A classical link is a link between any node in the

network that is capable of carrying classical network traffic.

Note that passive elements, such as optical switches, do not destroy

the quantum state. Therefore, it is possible to connect multiple

quantum nodes with each other over an optical network and perform

optical switching rather than routing via entanglement swapping at

quantum routers. This does require coordination with the elementary

link entanglement generation process, and it still requires repeaters

to overcome the short-distance limitations. However, this is a

potentially feasible architecture for local area networks.

### 5.3.3. Putting It All Together

A two-hop path in a generic quantum network can be represented as

follows:

+-----+ +-----+

| App |- - - - - - - - - -CC- - - - - - - - - -| App |

+-----+ +------+ +-----+

| EN |------ CL ------| QR |------ CL ------| EN |

| |------ QL ------| |------ QL ------| |

+-----+ +------+ +-----+

App - user-level application

EN - End Node

QL - Quantum Link

CL - Classical Link

CC - Classical Channel (traverses one or more CLs)

QR - Quantum Repeater

An application (App) running on two End Nodes (ENs) attached to a

network will at some point need the network to generate entangled

pairs for its use. This may require negotiation between the ENs

(possibly ahead of time), because they must both open a communication

end-point that the network can use to identify the two ends of the

connection. The two ENs use a Classical Channel (CC) available in

the network to achieve this goal.

When the network receives a request to generate end-to-end entangled

pairs, it uses the Classical Links (CLs) to coordinate and claim the

resources necessary to fulfill this request. This may be some

combination of prior control information (e.g., routing tables) and

signalling protocols, but the details of how this is achieved are an

active research question. A thought experiment on what this might

look like be can be found in Section 7.

During or after the distribution of control information, the network

performs the necessary quantum operations, such as generating

entanglement over individual Quantum Links (QLs), performing

entanglement swaps at Quantum Repeaters (QRs), and further signalling

to transmit the swap outcomes and other control information. Since

Bell pairs do not carry any user data, some of these operations can

be performed before the request is received, in anticipation of the

demand.

Note that here, "signalling" is used in a very broad sense and covers

many different types of messaging necessary for entanglement

generation control. For example, heralded entanglement generation

requires very precise timing synchronisation between the neighbouring

nodes, and thus the triggering of entanglement generation and

heralding may happen over its own, perhaps physically separate, CL,

as was the case in the network stack demonstration described in

[Pompili21.2]. Higher-level signalling with timing requirements that

are less stringent (e.g., control plane signalling) may then happen

over its own CL.

The entangled pair is delivered to the application once it is ready,

together with the relevant pair identifier. However, being ready

does not necessarily mean that all link pairs and entanglement swaps

are complete, as some applications can start executing on an

incomplete pair. In this case, the remaining entanglement swaps will

propagate the actions across the network to the other end, sometimes

necessitating fixup operations at the EN.

## 5.4. Physical Constraints

The model above has effectively abstracted away the particulars of

the hardware implementation. However, certain physical constraints

need to be considered in order to build a practical network. Some of

these are fundamental constraints, and no matter how much the

technology improves, they will always need to be addressed. Others

are artifacts of the early stages of a new technology. Here, we

consider a highly abstract scenario and refer to [Wehner18] for

pointers to the physics literature.

### 5.4.1. Memory Lifetimes

In addition to discrete operations being imperfect, storing a qubit

in memory is also highly non-trivial. The main difficulty in

achieving persistent storage is that it is extremely challenging to

isolate a quantum system from the environment. The environment

introduces an uncontrollable source of noise into the system, which

affects the fidelity of the state. This process is known as

decoherence. Eventually, the state has to be discarded once its

fidelity degrades too much.

The memory lifetime depends on the particular physical setup, but the

highest achievable values in quantum network hardware are, as of

2020, on the order of seconds [Abobeih18], although a lifetime of a

minute has also been demonstrated for qubits not connected to a

quantum network [Bradley19]. These values have increased

tremendously over the lifetime of the different technologies and are

bound to keep increasing. However, if quantum networks are to be

realised in the near future, they need to be able to handle short

memory lifetimes -- for example, by reducing latency on critical

paths.

### 5.4.2. Rates

Entanglement generation on a link between two connected nodes is not

a very efficient process, and it requires many attempts to succeed

[Hensen15] [Dahlberg19]. For example, the highest achievable rates

of success between nitrogen-vacancy center nodes -- which, in

addition to entanglement generation are also capable of storing and

processing the resulting qubits -- are on the order of 10 Hz.

Combined with short memory lifetimes, this leads to very tight timing

windows to build up network-wide connectivity.

Other platforms have shown higher entanglement rates, but this

usually comes at the cost of other hardware capabilities, such as no

quantum memory and/or limited processing capabilities [Wei22].

Nevertheless, the current rates are not sufficient for practical

applications beyond simple experimental proofs of concept. However,

they are expected to improve over time as quantum network technology

evolves [Wei22].

### 5.4.3. Communication Qubits

Most physical architectures capable of storing qubits are only able

to generate entanglement using only a subset of available qubits

called communication qubits [Dahlberg19]. Once a Bell pair has been

generated using a communication qubit, its state can be transferred

into memory. This may impose additional limitations on the network.

In particular, if a given node has only one communication qubit, it

cannot simultaneously generate Bell pairs over two links. It must

generate entanglement over the links one at a time.

### 5.4.4. Homogeneity

At present, all existing quantum network implementations are

homogeneous, and they do not interface with each other. In general,

it is very challenging to combine different quantum information

processing technologies.

There are many different physical hardware platforms for implementing

quantum networking hardware. The different technologies differ in

how they store and manipulate qubits in memory and how they generate

entanglement across a link with their neighbours. For example,

hardware based on optical elements and atomic ensembles [Sangouard11]

is very efficient at generating entanglement at high rates but

provides limited processing capabilities once the entanglement is

generated. On the other hand, nitrogen-vacancy-based platforms

[Hensen15] or trapped ion platforms [Moehring07] offer a much greater

degree of control over the qubits but have a harder time generating

entanglement at high rates.

In order to overcome the weaknesses of the different platforms,

coupling the different technologies will help to build fully

functional networks. For example, end nodes may be implemented using

technology with good qubit processing capabilities to enable complex

applications, but automated quantum nodes that serve only to "repeat"

along a linear chain, where the processing logic is much simpler, can

be implemented with technologies that sacrifice processing

capabilities for higher entanglement rates at long distances

[Askarani21].

This point is further exacerbated by the fact that quantum computers

(i.e., end nodes in a quantum network) are often based on different

hardware platforms than quantum repeaters, thus requiring a coupling

(transduction) between the two. This is especially true for quantum

computers based on superconducting technology, which are challenging

to connect to optical networks. However, even trapped ion quantum

computers, which make up a platform that has shown promise for

quantum networking, will still need to connect to other platforms

that are better at creating entanglement at high rates over long

distances (hundreds of kilometres).

# 6. Architectural Principles

Given that the most practical way of realising quantum network

connectivity is using Bell pair and entanglement-swapping repeater

technology, what sort of principles should guide us in assembling

such networks such that they are functional, robust, efficient, and,

most importantly, will work? Furthermore, how do we design networks

so that they work under the constraints imposed by the hardware

available today but do not impose unnecessary burdens on future

technology?

As quantum networking is a completely new technology that is likely

to see many iterations over its lifetime, this document must not

serve as a definitive set of rules but merely as a general set of

recommended guidelines for the first generations of quantum networks

based on principles and observations made by the community. The

benefit of having a community-built document at this early stage is

that expertise in both quantum information and network architecture

is needed in order to successfully build a quantum internet.

## 6.1. Goals of a Quantum Internet

When outlining any set of principles, we must ask ourselves what

goals we want to achieve, as inevitably trade-offs must be made. So,

what sort of goals should drive a quantum network architecture? The

following list has been inspired by the history of computer

networking, and thus it is inevitably very similar to one that could

be produced for the classical Internet [Clark88]. However, whilst

the goals may be similar, the challenges involved are often

fundamentally different. The list will also most likely evolve with

time and the needs of its users.

1. Support distributed quantum applications.

This goal seems trivially obvious, but it makes a subtle, but

important, point that highlights a key difference between quantum

and classical networks. Ultimately, quantum data transmission is

not the goal of a quantum network -- it is only one possible

component of quantum application protocols that are more advanced

[Wehner18]. Whilst transmission certainly could be used as a

building block for all quantum applications, it is not the most

basic one possible. For example, entanglement-based QKD, the

most well-known quantum application protocol, only relies on the

stronger-than-classical correlations and inherent secrecy of

entangled Bell pairs and does not have to transmit arbitrary

quantum states [Ekert91].

The primary purpose of a quantum internet is to support

distributed quantum application protocols, and it is of utmost

importance that they can run well and efficiently. Thus, it is

important to develop performance metrics meaningful to

applications to drive the development of quantum network

protocols. For example, the Bell pair generation rate is

meaningless if one does not also consider their fidelity. It is

generally much easier to generate pairs of lower fidelity, but

quantum applications may have to make multiple reattempts or even

abort if the fidelity is too low. A review of the requirements

for different known quantum applications can be found in

[Wehner18], and an overview of use cases can be found in

[QI-Scenarios].

2. Support tomorrow's distributed quantum applications.

The only principle of the Internet that should survive

indefinitely is the principle of constant change [RFC1958].

Technical change is continuous, and the size and capabilities of

the quantum internet will change by orders of magnitude.

Therefore, it is an explicit goal that a quantum internet

architecture be able to embrace this change. We have the benefit

of having been witness to the evolution of the classical Internet

over several decades, and we have seen what worked and what did

not. It is vital for a quantum internet to avoid the need for

flag days (e.g., NCP to TCP/IP) or upgrades that take decades to

roll out (e.g., IPv4 to IPv6).

Therefore, it is important that any proposed architecture for

general-purpose quantum repeater networks can integrate new

devices and solutions as they become available. The architecture

should not be constrained due to considerations for early-stage

hardware and applications. For example, it is already possible

to run QKD efficiently on metropolitan-scale networks, and such

networks are already commercially available. However, they are

not based on quantum repeaters and thus will not be able to

easily transition to applications that are more sophisticated.

3. Support heterogeneity.

There are multiple proposals for realising practical quantum

repeater hardware, and they all have their advantages and

disadvantages. Some may offer higher Bell pair generation rates

on individual links at the cost of entanglement swap operations

that are more difficult. Other platforms may be good all around

but are more difficult to build.

In addition to physical boundaries, there may be distinctions in

how errors are managed (Section 4.4.3.3). These differences will

affect the content and semantics of messages that cross these

boundaries -- for both connection setup and real-time operation.

The optimal network configuration will likely leverage the

advantages of multiple platforms to optimise the provided

service. Therefore, it is an explicit goal to incorporate varied

hardware and technology support from the beginning.

4. Ensure security at the network level.

The question of security in quantum networks is just as critical

as it is in the classical Internet, especially since enhanced

security offered by quantum entanglement is one of the key

driving factors.

Fortunately, from an application's point of view, as long as the

underlying implementation corresponds to (or sufficiently

approximates) theoretical models of quantum cryptography, quantum

cryptographic protocols do not need the network to provide any

guarantees about the confidentiality or integrity of the

transmitted qubits or the generated entanglement (though they may

impose requirements on the classical channel, e.g., to be

authenticated [Wang21]). Instead, applications will leverage the

classical networks to establish the end-to-end security of the

results obtained from the processing of entangled qubits.

However, it is important to note that whilst classical networks

are necessary to establish these end-to-end guarantees, the

security relies on the properties of quantum entanglement. For

example, QKD uses classical information reconciliation [Tang19]

for error correction and privacy amplification [Elkouss11] for

generating the final secure key, but the raw bits that are fed

into these protocols must come from measuring entangled qubits

[Ekert91]. In another application, secure delegated quantum

computing, the client hides its computation from the server by

sending qubits to the server and then requesting (in a classical

message) that the server measure them in an encoded basis. The

client then decodes the results it receives from the server to

obtain the result of the computation [Broadbent10]. Once again,

whilst a classical network is used to achieve the goal of secure

computation, the remote computation is strictly quantum.

Nevertheless, whilst applications can ensure their own end-to-end

security, network protocols themselves should be security aware

in order to protect the network itself and limit disruption.

Whilst the applications remain secure, they are not necessarily

operational or as efficient in the presence of an attacker. For

example, if an attacker can measure every qubit between two

parties trying to establish a key using QKD, no secret key can be

generated. Security concerns in quantum networks are described

in more detail in [Satoh17] and [Satoh20].

5. Make them easy to monitor.

In order to manage, evaluate the performance of, or debug a

network, it is necessary to have the ability to monitor the

network while ensuring that there will be mechanisms in place to

protect the confidentiality and integrity of the devices

connected to it. Quantum networks bring new challenges in this

area, so it should be a goal of a quantum network architecture to

make this task easy.

The fundamental unit of quantum information, the qubit, cannot be

actively monitored, as any readout irreversibly destroys its

contents. One of the implications of this fact is that measuring

an individual pair's fidelity is impossible. Fidelity is

meaningful only as a statistical quantity that requires constant

monitoring of generated Bell pairs, achieved by sacrificing some

Bell pairs for use in tomography or other methods.

Furthermore, given one end of an entangled pair, it is impossible

to tell where the other qubit is without any additional classical

metadata. It is impossible to extract this information from the

qubits themselves. This implies that tracking entangled pairs

necessitates some exchange of classical information. This

information might include (i) a reference to the entangled pair

that allows distributed applications to coordinate actions on

qubits of the same pair and (ii) the two bits from each

entanglement swap necessary to identify the final state of the

Bell pair (Section 4.4.2).

6. Ensure availability and resilience.

Any practical and usable network, classical or quantum, must be

able to continue to operate despite losses and failures and be

robust to malicious actors trying to disable connectivity. A

difference between quantum and classical networks is that quantum

networks are composed of two types of data planes (quantum and

classical) and two types of channels (quantum and classical) that

must be considered. Therefore, availability and resilience will

most likely require a more advanced treatment than they do in

classical networks.

Note that privacy, whilst related to security, is not listed as an

explicit goal, because the privacy benefits will depend on the use

case. For example, QKD only provides increased security for the

distribution of symmetric keys [Bennett14] [Ekert91]. The handling,

manipulation, sharing, encryption, and decryption of data will remain

entirely classical, limiting the benefits to privacy that can be

gained from using a quantum network. On the other hand, there are

applications like blind quantum computation, which provides the user

with the ability to execute a quantum computation on a remote server

without the server knowing what the computation was or its input and

output [Fitzsimons17]. Therefore, privacy must be considered on a

per-application basis. An overview of quantum network use cases can

be found in [QI-Scenarios].

## 6.2. The Principles of a Quantum Internet

The principles support the goals but are not goals themselves. The

goals define what we want to build, and the principles provide a

guideline for how we might achieve this. The goals will also be the

foundation for defining any metric of success for a network

architecture, whereas the principles in themselves do not distinguish

between success and failure. For more information about design

considerations for quantum networks, see [VanMeter13.1] and

[Dahlberg19].

1. Entanglement is the fundamental service.

The key service that a quantum network provides is the

distribution of entanglement between the nodes in a network. All

distributed quantum applications are built on top of this key

resource. Applications such as clustered quantum computing,

distributed quantum computing, distributed quantum sensing

networks, and certain kinds of quantum secure networks all

consume quantum entanglement as a resource. Some applications

(e.g., QKD) simply measure the entangled qubits to obtain a

shared secret key [QKD]. Other applications (e.g., distributed

quantum computing) build abstractions and operations that are

more complex on the entangled qubits, e.g., distributed CNOT

gates [DistCNOT] or teleportation of arbitrary qubit states

[Teleportation].

A quantum network may also distribute multipartite entangled

states (entangled states of three or more qubits) [Meignant19],

which are useful for applications such as conference key

agreement [Murta20], distributed quantum computing [Cirac99],

secret sharing [Qin17], and clock synchronisation [Komar14],

though it is worth noting that multipartite entangled states can

also be constructed from multiple entangled pairs distributed

between the end nodes.

2. Bell pairs are indistinguishable.

Any two Bell pairs between the same two nodes are

indistinguishable for the purposes of an application, provided

they both satisfy its required fidelity threshold. This

observation is likely to be key in enabling a more optimal

allocation of resources in a network, e.g., for the purposes of

provisioning resources to meet application demand. However, the

qubits that make up the pair themselves are not

indistinguishable, and the two nodes operating on a pair must

coordinate to make sure they are operating on qubits that belong

to the same Bell pair.

3. Fidelity is part of the service.

In addition to being able to deliver Bell pairs to the

communication end-points, the Bell pairs must be of sufficient

fidelity. Unlike in classical networks, where most errors are

effectively eliminated before reaching the application, many

quantum applications only need imperfect entanglement to

function. However, quantum applications will generally have a

threshold for Bell pair fidelity below which they are no longer

able to operate. Different applications will have different

requirements for what fidelity they can work with. It is the

network's responsibility to balance the resource usage with

respect to the applications' requirements. It may be that it is

cheaper for the network to provide lower-fidelity pairs that are

just above the threshold required by the application than it is

to guarantee high-fidelity pairs to all applications regardless

of their requirements.

4. Time is an expensive resource.

Time is not the only resource that is in short supply

(communication qubits and memory are as well), but ultimately it

is the lifetime of quantum memories that imposes some of the most

difficult conditions for operating an extended network of quantum

nodes. Current hardware has low rates of Bell pair generation,

short memory lifetimes, and access to a limited number of

communication qubits. All these factors combined mean that even

a short waiting queue at some node could be enough for a Bell

pair to decohere or result in an end-to-end pair below an

application's fidelity threshold. Therefore, managing the idle

time of qubits holding live quantum states should be done

carefully -- ideally by minimising the idle time, but potentially

also by moving the quantum state for temporary storage to a

quantum memory with a longer lifetime.

5. Be flexible with regards to capabilities and limitations.

This goal encompasses two important points:

* First, the architecture should be able to function under the

physical constraints imposed by the current-generation

hardware. Near-future hardware will have low entanglement

generation rates, quantum memories able to hold a handful of

qubits at best, and decoherence rates that will render many

generated pairs unusable.

* Second, the architecture should not make it difficult to run

the network over any hardware that may come along in the

future. The physical capabilities of repeaters will improve,

and redeploying a technology is extremely challenging.

# 7. A Thought Experiment Inspired by Classical Networks

To conclude, we discuss a plausible quantum network architecture

inspired by MPLS. This is not an architecture proposal but rather a

thought experiment to give the reader an idea of what components are

necessary for a functional quantum network. We use classical MPLS as

a basis, as it is well known and understood in the networking

community.

Creating end-to-end Bell pairs between remote end-points is a

stateful distributed task that requires a lot of a priori

coordination. Therefore, a connection-oriented approach seems the

most natural for quantum networks. In connection-oriented quantum

networks, when two quantum application end-points wish to start

creating end-to-end Bell pairs, they must first create a Quantum

Virtual Circuit (QVC). As an analogy, in MPLS networks, end-points

must establish a Label Switched Path (LSP) before exchanging traffic.

Connection-oriented quantum networks may also support virtual

circuits with multiple end-points for creating multipartite

entanglement. As an analogy, MPLS networks have the concept of

multipoint LSPs for multicast.

When a quantum application creates a QVC, it can indicate Quality of

Service (QoS) parameters such as the required capacity in end-to-end

Bell Pairs Per Second (BPPS) and the required fidelity of the Bell

pairs. As an analogy, in MPLS networks, applications specify the

required bandwidth in Bits Per Second (BPS) and other constraints

when they create a new LSP.

Different applications will have different QoS requirements. For

example, applications such as QKD that don't need to process the

entangled qubits, and only need measure them and store the resulting

outcome, may require a large volume of entanglement but will be

tolerant of delay and jitter for individual pairs. On the other

hand, distributed/cloud quantum computing applications may need fewer

entangled pairs but instead may need all of them to be generated in

one go so that they can all be processed together before any of them

decohere.

Quantum networks need a routing function to compute the optimal path

(i.e., the best sequence of routers and links) for each new QVC. The

routing function may be centralised or distributed. In the latter

case, the quantum network needs a distributed routing protocol. As

an analogy, classical networks use routing protocols such as Open

Shortest Path First (OSPF) and Intermediate System to Intermediate

System (IS-IS). However, note that the definition of "shortest path"

/ "least cost" may be different in a quantum network to account for

its non-classical features, such as fidelity [VanMeter13.2].

Given the very scarce availability of resources in early quantum

networks, a Traffic Engineering (TE) function is likely to be

beneficial. Without TE, QVCs always use the shortest path. In this

case, the quantum network cannot guarantee that each quantum end-

point will get its Bell pairs at the required rate or fidelity. This

is analogous to "best effort" service in classical networks.

With TE, QVCs choose a path that is guaranteed to have the requested

resources (e.g., bandwidth in BPPS) available, taking into account

the capacity of the routers and links and also taking into account

the resources already consumed by other virtual circuits. As an

analogy, both OSPF and IS-IS have TE extensions to keep track of used

and available resources and can use Constrained Shortest Path First

(CSPF) to take resource availability and other constraints into

account when computing the optimal path.

The use of TE implies the use of Call Admission Control (CAC): the

network denies any virtual circuits for which it cannot guarantee the

requested quality of service a priori. Alternatively, the network

preempts lower-priority circuits to make room for a new circuit.

Quantum networks need a signalling function: once the path for a QVC

has been computed, signalling is used to install the "forwarding

rules" into the data plane of each quantum router on the path. The

signalling may be distributed, analogous to the Resource Reservation

Protocol (RSVP) in MPLS. Or, the signalling may be centralised,

similar to OpenFlow.

Quantum networks need an abstraction of the hardware for specifying

the forwarding rules. This allows us to decouple the control plane

(routing and signalling) from the data plane (actual creation of Bell

pairs). The forwarding rules are specified using abstract building

blocks such as "creating local Bell pairs", "swapping Bell pairs", or

"distillation of Bell pairs". As an analogy, classical networks use

abstractions that are based on match conditions (e.g., looking up

header fields in tables) and actions (e.g., modifying fields or

forwarding a packet to a specific interface). The data plane

abstractions in quantum networks will be very different from those in

classical networks due to the fundamental differences in technology

and the stateful nature of quantum networks. In fact, choosing the

right abstractions will be one of the biggest challenges when

designing interoperable quantum network protocols.

In quantum networks, control plane traffic (routing and signalling

messages) is exchanged over a classical channel, whereas data plane

traffic (the actual Bell pair qubits) is exchanged over a separate

quantum channel. This is in contrast to most classical networks,

where control plane traffic and data plane traffic share the same

channel and where a single packet contains both user fields and

header fields. There is, however, a classical analogy to the way

quantum networks work: generalised MPLS (GMPLS) networks use separate

channels for control plane traffic and data plane traffic.

Furthermore, GMPLS networks support data planes where there is no

such thing as data plane headers (e.g., Dense Wavelength Division

Multiplexing (DWDM) or Time-Division Multiplexing (TDM) networks).

# 8. Security Considerations

Security is listed as an explicit goal for the architecture; this

issue is addressed in Section 6.1. However, as this is an

Informational document, it does not propose any concrete mechanisms

to achieve these goals.

# 9. IANA Considerations

This document has no IANA actions.

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# Acknowledgements

The authors want to thank Carlo Delle Donne, Matthew Skrzypczyk, Axel

Dahlberg, Mathias van den Bossche, Patrick Gelard, Chonggang Wang,

Scott Fluhrer, Joey Salazar, Joseph Touch, and the rest of the QIRG

community as a whole for their very useful reviews and comments on

this document.

WK and SW acknowledge funding received from the EU Flagship on

Quantum Technologies, Quantum Internet Alliance (No. 820445).

rdv acknowledges support by the Air Force Office of Scientific

Research under award number FA2386-19-1-4038.

# Authors' Addresses

Wojciech Kozlowski

QuTech

Building 22

Lorentzweg 1

2628 CJ Delft

Netherlands

Email: w.kozlowski@tudelft.nl

Stephanie Wehner

QuTech

Building 22

Lorentzweg 1

2628 CJ Delft

Netherlands

Email: s.d.c.wehner@tudelft.nl

Rodney Van Meter

Keio University

5322 Endo, Fujisawa, Kanagawa

252-0882

Japan

Email: rdv@sfc.wide.ad.jp

Bruno Rijsman

Individual

Email: brunorijsman@gmail.com

Angela Sara Cacciapuoti

University of Naples Federico II

Department of Electrical Engineering and Information Technologies

Claudio 21

80125 Naples

Italy

Email: angelasara.cacciapuoti@unina.it

Marcello Caleffi

University of Naples Federico II

Department of Electrical Engineering and Information Technologies

Claudio 21

80125 Naples

Italy

Email: marcello.caleffi@unina.it

Shota Nagayama

Mercari, Inc.

Roppongi Hills Mori Tower 18F

6-10-1 Roppongi, Minato-ku, Tokyo

106-6118

Japan

Internet Research Task Force (IRTF) W. Kozlowski

Request for Comments: 9340 S. Wehner

Category: Informational QuTech

ISSN: 2070-1721 R. Van Meter

Keio University

B. Rijsman

Individual

A. S. Cacciapuoti

M. Caleffi

University of Naples Federico II

S. Nagayama

Mercari, Inc.

March 2023

Architectural Principles for a Quantum Internet

The vision of a quantum internet is to enhance existing Internet

technology by enabling quantum communication between any two points

on Earth. To achieve this goal, a quantum network stack should be

built from the ground up to account for the fundamentally new

properties of quantum entanglement. The first quantum entanglement

networks have been realised, but there is no practical proposal for

how to organise, utilise, and manage such networks. In this

document, we attempt to lay down the framework and introduce some

basic architectural principles for a quantum internet. This is

intended for general guidance and general interest. It is also

intended to provide a foundation for discussion between physicists

and network specialists. This document is a product of the Quantum

Internet Research Group (QIRG).

This document is not an Internet Standards Track specification; it is

published for informational purposes.

This document is a product of the Internet Research Task Force

(IRTF). The IRTF publishes the results of Internet-related research

and development activities. These results might not be suitable for

deployment. This RFC represents the consensus of the Quantum

Internet Research Group of the Internet Research Task Force (IRTF).

Documents approved for publication by the IRSG are not candidates for

any level of Internet Standard; see Section 2 of RFC 7841.

Information about the current status of this document, any errata,

and how to provide feedback on it may be obtained at

https://www.rfc-editor.org/info/rfc9340.

Copyright (c) 2023 IETF Trust and the persons identified as the

document authors. All rights reserved.

This document is subject to BCP 78 and the IETF Trust's Legal

Provisions Relating to IETF Documents

(https://trustee.ietf.org/license-info) in effect on the date of

publication of this document. Please review these documents

carefully, as they describe your rights and restrictions with respect

to this document.

1. Introduction

2. Quantum Information

2.1. Quantum State

2.2. Qubit

2.3. Multiple Qubits

3. Entanglement as the Fundamental Resource

4. Achieving Quantum Connectivity

4.1. Challenges

4.1.1. The Measurement Problem

4.1.2. No-Cloning Theorem

4.1.3. Fidelity

4.1.4. Inadequacy of Direct Transmission

4.2. Bell Pairs

4.3. Teleportation

4.4. The Life Cycle of Entanglement

4.4.1. Elementary Link Generation

4.4.2. Entanglement Swapping

4.4.3. Error Management

4.4.4. Delivery

5. Architecture of a Quantum Internet

5.1. Challenges

5.2. Classical Communication

5.3. Abstract Model of the Network

5.3.1. The Control Plane and the Data Plane

5.3.2. Elements of a Quantum Network

5.3.3. Putting It All Together

5.4. Physical Constraints

5.4.1. Memory Lifetimes

5.4.2. Rates

5.4.3. Communication Qubits

5.4.4. Homogeneity

6. Architectural Principles

6.1. Goals of a Quantum Internet

6.2. The Principles of a Quantum Internet

7. A Thought Experiment Inspired by Classical Networks

8. Security Considerations

9. IANA Considerations

10. Informative References

Acknowledgements

Quantum networks are distributed systems of quantum devices that

utilise fundamental quantum mechanical phenomena such as

superposition, entanglement, and quantum measurement to achieve

capabilities beyond what is possible with non-quantum (classical)

networks [Kimble08]. Depending on the stage of a quantum network

[Wehner18], such devices may range from simple photonic devices

capable of preparing and measuring only one quantum bit (qubit) at a

time all the way to large-scale quantum computers of the future. A

quantum network is not meant to replace classical networks but rather

to form an overall hybrid classical-quantum network supporting new

capabilities that are otherwise impossible to realise [VanMeterBook].

For example, the most well-known application of quantum

communication, Quantum Key Distribution (QKD) [QKD], can create and

distribute a pair of symmetric encryption keys in such a way that the

security of the entire process relies on the laws of physics (and

thus can be mathematically proven to be unbreakable) rather than the

intractability of certain mathematical problems [Bennett14]

[Ekert91]. Small networks capable of QKD have even already been

deployed at short (roughly 100-kilometre) distances [Elliott03]

[Peev09] [Aguado19] [Joshi20].

The quantum networking paradigm also offers promise for a range of

new applications beyond quantum cryptography, such as distributed

quantum computation [Cirac99] [Crepeau02]; secure quantum computing

in the cloud [Fitzsimons17]; quantum-enhanced measurement networks

[Giovannetti04]; or higher-precision, long-baseline telescopes

[Gottesman12]. These applications are much more demanding than QKD,

and networks capable of executing them are in their infancy. The

first fully quantum, multinode network capable of sending, receiving,

and manipulating distributed quantum information has only recently

been realised [Pompili21.1].

Whilst a lot of effort has gone into physically realising and

connecting such devices, and making improvements to their speed and

error tolerance, no proposals for how to run these networks have been

worked out at the time of this writing. To draw an analogy with a

classical network, we are at a stage where we can start to physically

connect our devices and send data, but all sending, receiving, buffer

management, connection synchronisation, and so on must be managed by

the application directly by using low-level, custom-built, and

hardware-specific interfaces, rather than being managed by a network

stack that exposes a convenient high-level interface, such as

sockets. Only recently was the first-ever attempt at such a network

stack experimentally demonstrated in a laboratory setting

[Pompili21.2]. Furthermore, whilst physical mechanisms for

transmitting quantum information exist, there are no robust protocols

for managing such transmissions.

This document, produced by the Quantum Internet Research Group

(QIRG), introduces quantum networks and presents general guidelines

for the design and construction of such networks. Overall, it is

intended as an introduction to the subject for network engineers and

researchers. It should not be considered as a conclusive statement

on how quantum networks should or will be implemented. This document

was discussed on the QIRG mailing list and several IETF meetings. It

represents the consensus of the QIRG members, of both experts in the

subject matter (from the quantum and networking domains) and

newcomers who are the target audience.

In order to understand the framework for quantum networking, a basic

understanding of quantum information theory is necessary. The

following sections aim to introduce the minimum amount of knowledge

necessary to understand the principles of operation of a quantum

network. This exposition was written with a classical networking

audience in mind. It is assumed that the reader has never before

been exposed to any quantum physics. We refer the reader to

[SutorBook] and [NielsenChuang] for an in-depth introduction to

quantum information systems.

A quantum mechanical system is described by its quantum state. A

quantum state is an abstract object that provides a complete

description of the system at that particular moment. When combined

with the rules of the system's evolution in time, such as a quantum

circuit, it also then provides a complete description of the system

at all times. For the purposes of computing and networking, the

classical equivalent of a quantum state would be a string or stream

of logical bit values. These bits provide a complete description of

what values we can read out from that string at that particular

moment, and when combined with its rules for evolution in time, such

as a logical circuit, we will also know its value at any other time.

Just like a single classical bit, a quantum mechanical system can be

simple and consist of a single particle, e.g., an atom or a photon of

light. In this case, the quantum state provides the complete

description of that one particle. Similarly, just like a string of

bits consists of multiple bits, a single quantum state can be used to

also describe an ensemble of many particles. However, because

quantum states are governed by the laws of quantum mechanics, their

behaviour is significantly different to that of a string of bits. In

this section, we will summarise the key concepts to understand these

differences. We will then explain their consequences for networking

in the rest of this document.

The differences between quantum computation and classical computation

begin at the bit level. A classical computer operates on the binary

alphabet { 0, 1 }. A quantum bit, called a qubit, exists over the

same binary space, but unlike the classical bit, its state can exist

in a superposition of the two possibilities:

|qubit⟩ = a |0⟩ + b |1⟩,

where |X⟩ is Dirac's ket notation for a quantum state (the value that

a qubit holds) -- here, the binary 0 and 1 -- and the coefficients a

and b are complex numbers called probability amplitudes. Physically,

such a state can be realised using a variety of different

technologies such as electron spin, photon polarisation, atomic

energy levels, and so on.

Upon measurement, the qubit loses its superposition and irreversibly

collapses into one of the two basis states, either |0⟩ or |1⟩. Which

of the two states it ends up in may not be deterministic but can be

determined from the readout of the measurement. The measurement

result is a classical bit, 0 or 1, corresponding to |0⟩ and |1⟩,

respectively. The probability of measuring the state in the |0⟩

state is |a|^2; similarly, the probability of measuring the state in

the |1⟩ state is |b|^2, where |a|^2 + |b|^2 = 1. This randomness is

not due to our ignorance of the underlying mechanisms but rather is a

fundamental feature of a quantum mechanical system [Aspect81].

The superposition property plays an important role in fundamental

gate operations on qubits. Since a qubit can exist in a

superposition of its basis states, the elementary quantum gates are

able to act on all states of the superposition at the same time. For

example, consider the NOT gate:

NOT (a |0⟩ + b |1⟩) → a |1⟩ + b |0⟩.

It is important to note that "qubit" can have two meanings. In the

first meaning, "qubit" refers to a physical quantum *system* whose

quantum state can be expressed as a superposition of two basis

states, which we often label |0⟩ and |1⟩. Here, "qubit" refers to a

physical implementation akin to what a flip-flop, switch, voltage, or

current would be for a classical bit. In the second meaning, "qubit"

refers to the abstract quantum *state* of a quantum system with such

two basis states. In this case, the meaning of "qubit" is akin to

the logical value of a bit, from classical computing, i.e., "logical

0" or "logical 1". The two concepts are related, because a physical

"qubit" (first meaning) can be used to store the abstract "qubit"

(second meaning). Both meanings are used interchangeably in

literature, and the meaning is generally clear from the context.

When multiple qubits are combined in a single quantum state, the

space of possible states grows exponentially and all these states can

coexist in a superposition. For example, the general form of a two-

qubit register is

a |00⟩ + b |01⟩ + c |10⟩ + d |11⟩,

where the coefficients have the same probability amplitude

interpretation as for the single-qubit state. Each state represents

a possible outcome of a measurement of the two-qubit register. For

example, |01⟩ denotes a state in which the first qubit is in the

state |0⟩ and the second is in the state |1⟩.

Performing single-qubit gates affects the relevant qubit in each of

the superposition states. Similarly, two-qubit gates also act on all

the relevant superposition states, but their outcome is far more

interesting.

Consider a two-qubit register where the first qubit is in the

superposed state (|0⟩ + |1⟩)/sqrt(2) and the other is in the

state |0⟩. This combined state can be written as

(|0⟩ + |1⟩)/sqrt(2) x |0⟩ = (|00⟩ + |10⟩)/sqrt(2),

where x denotes a tensor product (the mathematical mechanism for

combining quantum states together).

The constant 1/sqrt(2) is called the normalisation factor and

reflects the fact that the probabilities of measuring either a |0⟩ or

a |1⟩ for the first qubit add up to one.

Let us now consider the two-qubit Controlled NOT, or CNOT, gate. The

CNOT gate takes as input two qubits -- a control and a target -- and

applies the NOT gate to the target if the control qubit is set. The

truth table looks like

+====+=====+

| IN | OUT |

+====+=====+

| 00 | 00 |

+----+-----+

| 01 | 01 |

+----+-----+

| 10 | 11 |

+----+-----+

| 11 | 10 |

+----+-----+

Table 1: CNOT Truth Table

Now, consider performing a CNOT gate on the state with the first

qubit being the control. We apply a two-qubit gate on all the

superposition states:

CNOT (|00⟩ + |10⟩)/sqrt(2) → (|00⟩ + |11⟩)/sqrt(2).

What is so interesting about this two-qubit gate operation? The

final state is *entangled*. There is no possible way of representing

that quantum state as a product of two individual qubits; they are no

longer independent. That is, it is not possible to describe the

quantum state of either of the individual qubits in a way that is

independent of the other qubit. Only the quantum state of the system

that consists of both qubits provides a physically complete

description of the two-qubit system. The states of the two

individual qubits are now correlated beyond what is possible to

achieve classically. Neither qubit is in a definite |0⟩ or |1⟩

state, but if we perform a measurement on either one, the outcome of

the partner qubit will *always* yield the exact same outcome. The

final state, whether it's |00⟩ or |11⟩, is fundamentally random as

before, but the states of the two qubits following a measurement will

always be identical. One can think of this as flipping two coins,

but both coins always land on "heads" or both land on "tails"

together -- something that we know is impossible classically.

Once a measurement is performed, the two qubits are once again

independent. The final state is either |00⟩ or |11⟩, and both of

these states can be trivially decomposed into a product of two

individual qubits. The entanglement has been consumed, and the

entangled state must be prepared again.

Entanglement is the fundamental building block of quantum networks.

Consider the state from the previous section:

(|00⟩ + |11⟩)/sqrt(2).

Neither of the two qubits is in a definite |0⟩ or |1⟩ state, and we

need to know the state of the entire register to be able to fully

describe the behaviour of the two qubits.

Entangled qubits have interesting non-local properties. Consider

sending one of the qubits to another device. This device could in

principle be anywhere: on the other side of the room, in a different

country, or even on a different planet. Provided negligible noise

has been introduced, the two qubits will forever remain in the

entangled state until a measurement is performed. The physical

distance does not matter at all for entanglement.

This lies at the heart of quantum networking, because it is possible

to leverage the non-classical correlations provided by entanglement

in order to design completely new types of application protocols that

are not possible to achieve with just classical communication.

Examples of such applications are quantum cryptography [Bennett14]

[Ekert91], blind quantum computation [Fitzsimons17], or distributed

quantum computation [Crepeau02].

Entanglement has two very special features from which one can derive

some intuition about the types of applications enabled by a quantum

network.

The first stems from the fact that entanglement enables stronger-

than-classical correlations, leading to opportunities for tasks that

require coordination. As a trivial example, consider the problem of

consensus between two nodes who want to agree on the value of a

single bit. They can use the quantum network to prepare the state

(|00⟩ + |11⟩)/sqrt(2) with each node holding one of the two qubits.

Once either of the two nodes performs a measurement, the state of the

two qubits collapses to either |00⟩ or |11⟩, so whilst the outcome is

random and does not exist before measurement, the two nodes will

always measure the same value. We can also build the more general

multi-qubit state (|00...⟩ + |11...⟩)/sqrt(2) and perform the same

algorithm between an arbitrary number of nodes. These stronger-than-

classical correlations generalise to measurement schemes that are

more complicated as well.

The second feature of entanglement is that it cannot be shared, in

the sense that if two qubits are maximally entangled with each other,

then it is physically impossible for these two qubits to also be

entangled with a third qubit [Terhal04]. Hence, entanglement forms a

sort of private and inherently untappable connection between two

nodes once established.

Entanglement is created through local interactions between two qubits

or as a product of the way the qubits were created (e.g., entangled

photon pairs). To create a distributed entangled state, one can then

physically send one of the qubits to a remote node. It is also

possible to directly entangle qubits that are physically separated,

but this still requires local interactions between some other qubits

that the separated qubits are initially entangled with. Therefore,

it is the transmission of qubits that draws the line between a

genuine quantum network and a collection of quantum computers

connected over a classical network.

A quantum network is defined as a collection of nodes that is able to

exchange qubits and distribute entangled states amongst themselves.

A quantum node that is able only to communicate classically with

another quantum node is not a member of a quantum network.

Services and applications that are more complex can be built on top

of entangled states distributed by the network; for example, see

[ZOO].

This section explains the meaning of quantum connectivity and the

necessary physical processes at an abstract level.

A quantum network cannot be built by simply extrapolating all the

classical models to their quantum analogues. Sending qubits over a

wire like we send classical bits is simply not as easy to do. There

are several technological as well as fundamental challenges that make

classical approaches unsuitable in a quantum context.

In classical computers and networks, we can read out the bits stored

in memory at any time. This is helpful for a variety of purposes

such as copying, error detection and correction, and so on. This is

not possible with qubits.

A measurement of a qubit's state will destroy its superposition and

with it any entanglement it may have been part of. Once a qubit is

being processed, it cannot be read out until a suitable point in the

computation, determined by the protocol handling the qubit, has been

reached. Therefore, we cannot use the same methods known from

classical computing for the purposes of error detection and

correction. Nevertheless, quantum error detection and correction

schemes exist that take this problem into account, and how a network

chooses to manage errors will have an impact on its architecture.

Since directly reading the state of a qubit is not possible, one

could ask if we can simply copy a qubit without looking at it.

Unfortunately, this is fundamentally not possible in quantum

mechanics [Park70] [Wootters82].

The no-cloning theorem states that it is impossible to create an

identical copy of an arbitrary, unknown quantum state. Therefore, it

is also impossible to use the same mechanisms that worked for

classical networks for signal amplification, retransmission, and so

on, as they all rely on the ability to copy the underlying data.

Since any physical channel will always be lossy, connecting nodes

within a quantum network is a challenging endeavour, and its

architecture must at its core address this very issue.

In general, it is expected that a classical packet arrives at its

destination without any errors introduced by hardware noise along the

way. This is verified at various levels through a variety of error

detection and correction mechanisms. Since we cannot read or copy a

quantum state, error detection and correction are more involved.

To describe the quality of a quantum state, a physical quantity

called fidelity is used [NielsenChuang]. Fidelity takes a value

between 0 and 1 -- higher is better, and less than 0.5 means the

state is unusable. It measures how close a quantum state is to the

state we have tried to create. It expresses the probability that the

state will behave exactly the same as our desired state. Fidelity is

an important property of a quantum system that allows us to quantify

how much a particular state has been affected by noise from various

sources (gate errors, channel losses, environment noise).

Interestingly, quantum applications do not need perfect fidelity to

be able to execute -- as long as the fidelity is above some

application-specific threshold, they will simply operate at lower

rates. Therefore, rather than trying to ensure that we always

deliver perfect states (a technologically challenging task),

applications will specify a minimum threshold for the fidelity, and

the network will try its best to deliver it. A higher fidelity can

be achieved by either having hardware produce states of better

fidelity (sometimes one can sacrifice rate for higher fidelity) or

employing quantum error detection and correction mechanisms (see

[Mural16] and Chapter 11 of [VanMeterBook]).

Conceptually, the most straightforward way to distribute an entangled

state is to simply transmit one of the qubits directly to the other

end across a series of nodes while performing sufficient forward

Quantum Error Correction (QEC) (Section 4.4.3.2) to bring losses down

to an acceptable level. Despite the no-cloning theorem and the

inability to directly measure a quantum state, error-correcting

mechanisms for quantum communication exist [Jiang09] [Fowler10]

[Devitt13] [Mural16]. However, QEC makes very high demands on both

resources (physical qubits needed) and their initial fidelity.

Implementation is very challenging, and QEC is not expected to be

used until later generations of quantum networks are possible (see

Figure 2 of [Mural16] and Section 4.4.3.3 of this document). Until

then, quantum networks rely on entanglement swapping (Section 4.4.2)

and teleportation (Section 4.3). This alternative relies on the

observation that we do not need to be able to distribute any

arbitrary entangled quantum state. We only need to be able to

distribute any one of what are known as the Bell pair states

[Briegel98].

Bell pair states are the entangled two-qubit states:

|00⟩ + |11⟩,

|00⟩ - |11⟩,

|01⟩ + |10⟩,

|01⟩ - |10⟩,

where the constant 1/sqrt(2) normalisation factor has been ignored

for clarity. Any of the four Bell pair states above will do, as it

is possible to transform any Bell pair into another Bell pair with

local operations performed on only one of the qubits. When each

qubit in a Bell pair is held by a separate node, either node can

apply a series of single-qubit gates to their qubit alone in order to

transform the state between the different variants.

Distributing a Bell pair between two nodes is much easier than

transmitting an arbitrary quantum state over a network. Since the

state is known, handling errors becomes easier, and small-scale error

correction (such as entanglement distillation, as discussed in

Section 4.4.3.1), combined with reattempts, becomes a valid strategy.

The reason for using Bell pairs specifically as opposed to any other

two-qubit state is that they are the maximally entangled two-qubit

set of basis states. Maximal entanglement means that these states

have the strongest non-classical correlations of all possible two-

qubit states. Furthermore, since single-qubit local operations can

never increase entanglement, states that are less entangled would

impose some constraints on distributed quantum algorithms. This

makes Bell pairs particularly useful as a generic building block for

distributed quantum applications.

The observation that we only need to be able to distribute Bell pairs

relies on the fact that this enables the distribution of any other

arbitrary entangled state. This can be achieved via quantum state

teleportation [Bennett93]. Quantum state teleportation consumes an

unknown qubit state that we want to transmit and recreates it at the

desired destination. This does not violate the no-cloning theorem,

as the original state is destroyed in the process.

To achieve this, an entangled pair needs to be distributed between

the source and destination before teleportation commences. The

source then entangles the transmission qubit with its end of the pair

and performs a readout of the two qubits (the sum of these operations

is called a Bell state measurement). This consumes the Bell pair's

entanglement, turning the source and destination qubits into

independent states. The measurement yields two classical bits, which

the source sends to the destination over a classical channel. Based

on the value of the received two classical bits, the destination

performs one of four possible corrections (called the Pauli

corrections) on its end of the pair, which turns it into the unknown

qubit state that we wanted to transmit. This requirement to

communicate the measurement readout over a classical channel

unfortunately means that entanglement cannot be used to transmit

information faster than the speed of light.

The unknown quantum state that was transmitted was never fed into the

network itself. Therefore, the network needs to only be able to

reliably produce Bell pairs between any two nodes in the network.

Thus, a key difference between a classical data plane and a quantum

data plane is that a classical data plane carries user data but a

quantum data plane provides the resources for the user to transmit

user data themselves without further involvement of the network.

Reducing the problem of quantum connectivity to one of generating a

Bell pair has reduced the problem to a simpler, more fundamental

case, but it has not solved it. In this section, we discuss how

these entangled pairs are generated in the first place and how their

two qubits are delivered to the end-points.

In a quantum network, entanglement is always first generated locally

(at a node or an auxiliary element), followed by a movement of one or

both of the entangled qubits across the link through quantum

channels. In this context, photons (particles of light) are the

natural candidate for entanglement carriers. Because these photons

carry quantum states from place to place at high speed, we call them

flying qubits. The rationale for this choice is related to the

advantages provided by photons, such as moderate interaction with the

environment leading to moderate decoherence; convenient control with

standard optical components; and high-speed, low-loss transmissions.

However, since photons are hard to store, a transducer must transfer

the flying qubit's state to a qubit suitable for information

processing and/or storage (often referred to as a matter qubit).

Since this process may fail, in order to generate and store

entanglement efficiently, we must be able to distinguish successful

attempts from failures. Entanglement generation schemes that are

able to announce successful generation are called heralded

entanglement generation schemes.

There exist three basic schemes for heralded entanglement generation

on a link through coordinated action of the two nodes at the two ends

of the link [Cacciapuoti19]:

"At mid-point": In this scheme, an entangled photon pair source

sitting midway between the two nodes with matter qubits sends an

entangled photon through a quantum channel to each of the nodes.

There, transducers are invoked to transfer the entanglement from

the flying qubits to the matter qubits. In this scheme, the

transducers know if the transfers succeeded and are able to herald

successful entanglement generation via a message exchange over the

classical channel.

"At source": In this scheme, one of the two nodes sends a flying

qubit that is entangled with one of its matter qubits. A

transducer at the other end of the link will transfer the

entanglement from the flying qubit to one of its matter qubits.

Just like in the previous scheme, the transducer knows if its

transfer succeeded and is able to herald successful entanglement

generation with a classical message sent to the other node.

"At both end-points": In this scheme, both nodes send a flying qubit

that is entangled with one of their matter qubits. A detector

somewhere in between the nodes performs a joint measurement on the

flying qubits, which stochastically projects the remote matter

qubits into an entangled quantum state. The detector knows if the

entanglement succeeded and is able to herald successful

entanglement generation by sending a message to each node over the

classical channel.

The "mid-point source" scheme is more robust to photon loss, but in

the other schemes, the nodes retain greater control over the

entangled pair generation.

Note that whilst photons travel in a particular direction through the

quantum channel the resulting entangled pair of qubits does not have

a direction associated with it. Physically, there is no upstream or

downstream end of the pair.

The problem with generating entangled pairs directly across a link is

that efficiency decreases with channel length. Beyond a few tens of

kilometres in optical fibre or 1000 kilometres in free space (via

satellite), the rate is effectively zero, and due to the no-cloning

theorem we cannot simply amplify the signal. The solution is

entanglement swapping [Briegel98].

A Bell pair between any two nodes in the network can be constructed

by combining the pairs generated along each individual link on a path

between the two end-points. Each node along the path can consume the

two pairs on the two links to which it is connected, in order to

produce a new entangled pair between the two remote ends. This

process is known as entanglement swapping. It can be represented

pictorially as follows:

+---------+ +---------+ +---------+

| A | | B | | C |

| |------| |------| |

| X1~~~~~~~~~~X2 Y1~~~~~~~~~~Y2 |

+---------+ +---------+ +---------+

where X1 and X2 are the qubits of the entangled pair X and Y1 and Y2

are the qubits of entangled pair Y. The entanglement is denoted with

~~. In the diagram above, nodes A and B share the pair X and nodes B

and C share the pair Y, but we want entanglement between A and C.

To achieve this goal, we simply teleport the qubit X2 using the pair

Y. This requires node B to perform a Bell state measurement on the

qubits X2 and Y1 that results in the destruction of the entanglement

between Y1 and Y2. However, X2 is recreated in Y2's place, carrying

with it its entanglement with X1. The end result is shown below:

+---------+ +---------+ +---------+

| A | | B | | C |

| |------| |------| |

| X1~~~~~~~~~~~~~~~~~~~~~~~~~~~X2 |

+---------+ +---------+ +---------+

Depending on the needs of the network and/or application, a final

Pauli correction at the recipient node may not be necessary, since

the result of this operation is also a Bell pair. However, the two

classical bits that form the readout from the measurement at node B

must still be communicated, because they carry information about

which of the four Bell pairs was actually produced. If a correction

is not performed, the recipient must be informed which Bell pair was

received.

This process of teleporting Bell pairs using other entangled pairs is

called entanglement swapping. Quantum nodes that create long-

distance entangled pairs via entanglement swapping are called quantum

repeaters in academic literature [Briegel98]. We will use the same

terminology in this document.

Neither the generation of Bell pairs nor the swapping operations are

noiseless operations. Therefore, with each link and each swap, the

fidelity of the state degrades. However, it is possible to create

higher-fidelity Bell pair states from two or more lower-fidelity

pairs through a process called distillation (sometimes also referred

to as purification) [Dur07].

To distil a quantum state, a second (and sometimes third) quantum

state is used as a "test tool" to test a proposition about the first

state, e.g., "the parity of the two qubits in the first state is

even." When the test succeeds, confidence in the state is improved,

and thus the fidelity is improved. The test tool states are

destroyed in the process, so resource demands increase substantially

when distillation is used. When the test fails, the tested state

must also be discarded. Distillation makes low demands on fidelity

and resources compared to QEC, but distributed protocols incur round-

trip delays due to classical communication [Bennett96].

Just like classical error correction, QEC encodes logical qubits

using several physical (raw) qubits to protect them from the errors

described in Section 4.1.3 [Jiang09] [Fowler10] [Devitt13] [Mural16].

Furthermore, similarly to its classical counterpart, QEC can not only

correct state errors but also account for lost qubits. Additionally,

if all physical qubits that encode a logical qubit are located at the

same node, the correction procedure can be executed locally, even if

the logical qubit is entangled with remote qubits.

Although QEC was originally a scheme proposed to protect a qubit from

noise, QEC can also be applied to entanglement distillation. Such

QEC-applied distillation is cost effective but requires a higher base

fidelity.

Quantum networks have been categorised into three "generations" based

on the error management scheme they employ [Mural16]. Note that

these "generations" are more like categories; they do not necessarily

imply a time progression and do not obsolete each other, though the

later generations do require technologies that are more advanced.

Which generation is used depends on the hardware platform and network

design choices.

Table 2 summarises the generations.

+===========+================+=======================+=============+

| | First | Second generation | Third |

| | generation | | generation |

+===========+================+=======================+=============+

| Loss | Heralded | Heralded entanglement | QEC (no |

| tolerance | entanglement | generation | classical |

| | generation | (bidirectional | signalling) |

| | (bidirectional | classical signalling) | |

| | classical | | |

| | signalling) | | |

+-----------+----------------+-----------------------+-------------+

+-----------+----------------+-----------------------+-------------+

| Error | Entanglement | Entanglement | QEC (no |

| tolerance | distillation | distillation | classical |

| | (bidirectional | (unidirectional | signalling) |

| | classical | classical signalling) | |

| | signalling) | or QEC (no classical | |

| | | signalling) | |

+-----------+----------------+-----------------------+-------------+

Table 2: Classical Signalling and Generations

Generations are defined by the directions of classical signalling

required in their distributed protocols for loss tolerance and error

tolerance. Classical signalling carries the classical bits,

incurring round-trip delays. As described in Section 4.4.3.1, these

delays affect the performance of quantum networks, especially as the

distance between the communicating nodes increases.

Loss tolerance is about tolerating qubit transmission losses between

nodes. Heralded entanglement generation, as described in

Section 4.4.1, confirms the receipt of an entangled qubit using a

heralding signal. A pair of directly connected quantum nodes

repeatedly attempt to generate an entangled pair until the heralding

signal is received. As described in Section 4.4.3.2, QEC can be

applied to complement lost qubits, eliminating the need for

reattempts. Furthermore, since the correction procedure is composed

of local operations, it does not require a heralding signal.

However, it is possible only when the photon loss rate from

transmission to measurement is less than 50%.

Error tolerance is about tolerating quantum state errors.

Entanglement distillation is the easiest mechanism to implement for

improved error tolerance, but it incurs round-trip delays due to the

requirement for bidirectional classical signalling. The alternative,

QEC, is able to correct state errors locally so that it does not need

any classical signalling between the quantum nodes. In between these

two extremes, there is also QEC-applied distillation, which requires

unidirectional classical signalling.

The three "generations" summarised:

1. First-generation quantum networks use heralding for loss

tolerance and entanglement distillation for error tolerance.

These networks can be implemented even with a limited set of

available quantum gates.

2. Second-generation quantum networks improve upon the first

generation with QEC codes for error tolerance (but not loss

tolerance). At first, QEC will be applied to entanglement

distillation only, which requires unidirectional classical

signalling. Later, QEC codes will be used to create logical Bell

pairs that no longer require any classical signalling for the

purposes of error tolerance. Heralding is still used to

compensate for transmission losses.

3. Third-generation quantum networks directly transmit QEC-encoded

qubits to adjacent nodes, as discussed in Section 4.1.4.

Elementary link Bell pairs can now be created without heralding

or any other classical signalling. Furthermore, this also

enables direct transmission architectures in which qubits are

forwarded end to end like classical packets rather than relying

on Bell pairs and entanglement swapping.

Despite the fact that there are important distinctions in how errors

will be managed in the different generations, it is unlikely that all

quantum networks will consistently use the same method. This is due

to different hardware requirements of the different generations and

the practical reality of network upgrades. Therefore, it is

unavoidable that eventually boundaries between different error

management schemes start forming. This will affect the content and

semantics of messages that must cross those boundaries -- for both

connection setup and real-time operation [Nagayama16].

Eventually, the Bell pairs must be delivered to an application (or

higher-layer protocol) at the two end nodes. A detailed list of such

requirements is beyond the scope of this document. At minimum, the

end nodes require information to map a particular Bell pair to the

qubit in their local memory that is part of this entangled pair.

It is evident from the previous sections that the fundamental service

provided by a quantum network significantly differs from that of a

classical network. Therefore, it is not surprising that the

architecture of a quantum internet will itself be very different from

that of the classical Internet.

This subsection covers the major fundamental challenges involved in

building quantum networks. Here, we only describe the fundamental

differences. Technological limitations are described in Section 5.4.

1. Bell pairs are not equivalent to packets that carry payload.

In most classical networks, including Ethernet, Internet Protocol

(IP), and Multi-Protocol Label Switching (MPLS) networks, user

data is grouped into packets. In addition to the user data, each

packet also contains a series of headers that contain the control

information that lets routers and switches forward it towards its

destination. Packets are the fundamental unit in a classical

network.

In a quantum network, the entangled pairs of qubits are the basic

unit of networking. These qubits themselves do not carry any

headers. Therefore, quantum networks will have to send all

control information via separate classical channels, which the

repeaters will have to correlate with the qubits stored in their

memory. Furthermore, unlike a classical packet, which is located

at a single node, a Bell pair consists of two qubits distributed

across two nodes. This has a fundamental impact on how quantum

networks will be managed and how protocols need to be designed.

To make long-distance Bell pairs, the nodes may have to keep

their qubits in their quantum memories and wait until control

information is exchanged before proceeding with the next

operation. This signalling will result in additional latency,

which will depend on the distance between the nodes holding the

two ends of the Bell pair. Error management, such as

entanglement distillation, is a typical example of such control

information exchange [Nagayama21] (see also Section 4.4.3.3).

2. "Store and forward" and "store and swap" quantum networks require

different state management techniques.

As described in Section 4.4.1, quantum links provide Bell pairs

that are undirected network resources, in contrast to directed

frames of classical networks. This phenomenological distinction

leads to architectural differences between quantum networks and

classical networks. Quantum networks combine multiple elementary

link Bell pairs together to create one end-to-end Bell pair,

whereas classical networks deliver messages from one end to the

other end hop by hop.

Classical networks receive data on one interface, store it in

local buffers, and then forward the data to another appropriate

interface. Quantum networks store Bell pairs and then execute

entanglement swapping instead of forwarding in the data plane.

Such quantum networks are "store and swap" networks. In "store

and swap" networks, we do not need to care about the order in

which the Bell pairs were generated, since they are undirected.

However, whilst the ordering does not matter, it is very

important that the right entangled pairs get swapped, and that

the intermediate measurement outcomes (see Section 4.4.2) are

signalled to and correlated with the correct qubits at the other

nodes. Otherwise, the final end-to-end entangled pair will not

be created between the expected end-points or will be in a

different quantum state than expected. For example, rather than

Alice receiving a qubit that is entangled with Bob's qubit, her

qubit is entangled with Charlie's qubit. This distinction makes

control algorithms and optimisation of quantum networks different

from those for classical networks, in the sense that swapping is

stateful in contrast to stateless packet-by-packet forwarding.

Note that, as described in Section 4.4.3.3, third-generation

quantum networks will be able to support a "store and forward"

architecture in addition to "store and swap".

3. An entangled pair is only useful if the locations of both qubits

are known.

A classical network packet logically exists only at one location

at any point in time. If a packet is modified in some way,

whether headers or payload, this information does not need to be

conveyed to anybody else in the network. The packet can be

simply forwarded as before.

In contrast, entanglement is a phenomenon in which two or more

qubits exist in a physically distributed state. Operations on

one of the qubits change the mutual state of the pair. Since the

owner of a particular qubit cannot just read out its state, it

must coordinate all its actions with the owner of the pair's

other qubit. Therefore, the owner of any qubit that is part of

an entangled pair must know the location of its counterpart.

Location, in this context, need not be the explicit spatial

location. A relevant pair identifier, a means of communication

between the pair owners, and an association between the pair ID

and the individual qubits will be sufficient.

4. Generating entanglement requires temporary state.

Packet forwarding in a classical network is largely a stateless

operation. When a packet is received, the router does a lookup

in its forwarding table and sends the packet out of the

appropriate output. There is no need to keep any memory of the

packet any more.

A quantum node must be able to make decisions about qubits that

it receives and is holding in its memory. Since qubits do not

carry headers, the receipt of an entangled pair conveys no

control information based on which the repeater can make a

decision. The relevant control information will arrive

separately over a classical channel. This implies that a

repeater must store temporary state, as the control information

and the qubit it pertains to will, in general, not arrive at the

same time.

In this document, we have already covered two different roles that

classical communication must perform the following:

* Communicate classical bits of information as part of distributed

protocols such as entanglement swapping and teleportation.

* Communicate control information within a network, including

background protocols such as routing, as well as signalling

protocols to set up end-to-end entanglement generation.

Classical communication is a crucial building block of any quantum

network. All nodes in a quantum network are assumed to have

classical connectivity with each other (within typical administrative

domain limits). Therefore, quantum nodes will need to manage two

data planes in parallel: a classical data plane and a quantum data

plane. Additionally, a node must be able to correlate information

between the two planes so that the control information received on a

classical channel can be applied to the qubits managed by the quantum

data plane.

Control plane protocols for quantum networks will have many

responsibilities similar to their classical counterparts, namely

discovering the network topology, resource management, populating

data plane tables, etc. Most of these protocols do not require the

manipulation of quantum data and can operate simply by exchanging

classical messages only. There may also be some control plane

functionality that does require the handling of quantum data

[QI-Scenarios]. As it is not clear if there is much benefit in

defining a separate quantum control plane given the significant

overlap in responsibilities with its classical counterpart, the

question of whether there should be a separate quantum control plane

is beyond the scope of this document.

However, the data plane separation is much more distinct, and there

will be two data planes: a classical data plane and a quantum data

plane. The classical data plane processes and forwards classical

packets. The quantum data plane processes and swaps entangled pairs.

Third-generation quantum networks may also forward qubits in addition

to swapping Bell pairs.

In addition to control plane messages, there will also be control

information messages that operate at the granularity of individual

entangled pairs, such as heralding messages used for elementary link

generation (Section 4.4.1). In terms of functionality, these

messages are closer to classical packet headers than control plane

messages, and thus we consider them to be part of the quantum data

plane. Therefore, a quantum data plane also includes the exchange of

classical control information at the granularity of individual qubits

and entangled pairs.

We have identified quantum repeaters as the core building block of a

quantum network. However, a quantum repeater will have to do more

than just entanglement swapping in a functional quantum network. Its

key responsibilities will include the following:

1. Creating link-local entanglement between neighbouring nodes.

2. Extending entanglement from link-local pairs to long-range pairs

through entanglement swapping.

3. Performing distillation to manage the fidelity of the produced

pairs.

4. Participating in the management of the network (routing, etc.).

Not all quantum repeaters in the network will be the same; here, we

break them down further:

Quantum routers (controllable quantum nodes): A quantum router is a

quantum repeater with a control plane that participates in the

management of the network and will make decisions about which

qubits to swap to generate the requested end-to-end pairs.

Automated quantum nodes: An automated quantum node is a data-plane-

only quantum repeater that does not participate in the network

control plane. Since the no-cloning theorem precludes the use of

amplification, long-range links will be established by chaining

multiple such automated nodes together.

End nodes: End nodes in a quantum network must be able to receive

and handle an entangled pair, but they do not need to be able to

perform an entanglement swap (and thus are not necessarily quantum

repeaters). End nodes are also not required to have any quantum

memory, as certain quantum applications can be realised by having

the end node measure its qubit as soon as it is received.

Non-quantum nodes: Not all nodes in a quantum network need to have a

quantum data plane. A non-quantum node is any device that can

handle classical network traffic.

Additionally, we need to identify two kinds of links that will be

used in a quantum network:

Quantum links: A quantum link is a link that can be used to generate

an entangled pair between two directly connected quantum

repeaters. This may include additional mid-point elements as

described in Section 4.4.1. It may also include a dedicated

classical channel that is to be used solely for the purpose of

coordinating the entanglement generation on this quantum link.

Classical links: A classical link is a link between any node in the

network that is capable of carrying classical network traffic.

Note that passive elements, such as optical switches, do not destroy

the quantum state. Therefore, it is possible to connect multiple

quantum nodes with each other over an optical network and perform

optical switching rather than routing via entanglement swapping at

quantum routers. This does require coordination with the elementary

link entanglement generation process, and it still requires repeaters

to overcome the short-distance limitations. However, this is a

potentially feasible architecture for local area networks.

A two-hop path in a generic quantum network can be represented as

follows:

+-----+ +-----+

| App |- - - - - - - - - -CC- - - - - - - - - -| App |

+-----+ +------+ +-----+

| EN |------ CL ------| QR |------ CL ------| EN |

| |------ QL ------| |------ QL ------| |

+-----+ +------+ +-----+

App - user-level application

EN - End Node

QL - Quantum Link

CL - Classical Link

CC - Classical Channel (traverses one or more CLs)

QR - Quantum Repeater

An application (App) running on two End Nodes (ENs) attached to a

network will at some point need the network to generate entangled

pairs for its use. This may require negotiation between the ENs

(possibly ahead of time), because they must both open a communication

end-point that the network can use to identify the two ends of the

connection. The two ENs use a Classical Channel (CC) available in

the network to achieve this goal.

When the network receives a request to generate end-to-end entangled

pairs, it uses the Classical Links (CLs) to coordinate and claim the

resources necessary to fulfill this request. This may be some

combination of prior control information (e.g., routing tables) and

signalling protocols, but the details of how this is achieved are an

active research question. A thought experiment on what this might

look like be can be found in Section 7.

During or after the distribution of control information, the network

performs the necessary quantum operations, such as generating

entanglement over individual Quantum Links (QLs), performing

entanglement swaps at Quantum Repeaters (QRs), and further signalling

to transmit the swap outcomes and other control information. Since

Bell pairs do not carry any user data, some of these operations can

be performed before the request is received, in anticipation of the

demand.

Note that here, "signalling" is used in a very broad sense and covers

many different types of messaging necessary for entanglement

generation control. For example, heralded entanglement generation

requires very precise timing synchronisation between the neighbouring

nodes, and thus the triggering of entanglement generation and

heralding may happen over its own, perhaps physically separate, CL,

as was the case in the network stack demonstration described in

[Pompili21.2]. Higher-level signalling with timing requirements that

are less stringent (e.g., control plane signalling) may then happen

over its own CL.

The entangled pair is delivered to the application once it is ready,

together with the relevant pair identifier. However, being ready

does not necessarily mean that all link pairs and entanglement swaps

are complete, as some applications can start executing on an

incomplete pair. In this case, the remaining entanglement swaps will

propagate the actions across the network to the other end, sometimes

necessitating fixup operations at the EN.

The model above has effectively abstracted away the particulars of

the hardware implementation. However, certain physical constraints

need to be considered in order to build a practical network. Some of

these are fundamental constraints, and no matter how much the

technology improves, they will always need to be addressed. Others

are artifacts of the early stages of a new technology. Here, we

consider a highly abstract scenario and refer to [Wehner18] for

pointers to the physics literature.

In addition to discrete operations being imperfect, storing a qubit

in memory is also highly non-trivial. The main difficulty in

achieving persistent storage is that it is extremely challenging to

isolate a quantum system from the environment. The environment

introduces an uncontrollable source of noise into the system, which

affects the fidelity of the state. This process is known as

decoherence. Eventually, the state has to be discarded once its

fidelity degrades too much.

The memory lifetime depends on the particular physical setup, but the

highest achievable values in quantum network hardware are, as of

2020, on the order of seconds [Abobeih18], although a lifetime of a

minute has also been demonstrated for qubits not connected to a

quantum network [Bradley19]. These values have increased

tremendously over the lifetime of the different technologies and are

bound to keep increasing. However, if quantum networks are to be

realised in the near future, they need to be able to handle short

memory lifetimes -- for example, by reducing latency on critical

paths.

Entanglement generation on a link between two connected nodes is not

a very efficient process, and it requires many attempts to succeed

[Hensen15] [Dahlberg19]. For example, the highest achievable rates

of success between nitrogen-vacancy center nodes -- which, in

addition to entanglement generation are also capable of storing and

processing the resulting qubits -- are on the order of 10 Hz.

Combined with short memory lifetimes, this leads to very tight timing

windows to build up network-wide connectivity.

Other platforms have shown higher entanglement rates, but this

usually comes at the cost of other hardware capabilities, such as no

quantum memory and/or limited processing capabilities [Wei22].

Nevertheless, the current rates are not sufficient for practical

applications beyond simple experimental proofs of concept. However,

they are expected to improve over time as quantum network technology

evolves [Wei22].

Most physical architectures capable of storing qubits are only able

to generate entanglement using only a subset of available qubits

called communication qubits [Dahlberg19]. Once a Bell pair has been

generated using a communication qubit, its state can be transferred

into memory. This may impose additional limitations on the network.

In particular, if a given node has only one communication qubit, it

cannot simultaneously generate Bell pairs over two links. It must

generate entanglement over the links one at a time.

At present, all existing quantum network implementations are

homogeneous, and they do not interface with each other. In general,

it is very challenging to combine different quantum information

processing technologies.

There are many different physical hardware platforms for implementing

quantum networking hardware. The different technologies differ in

how they store and manipulate qubits in memory and how they generate

entanglement across a link with their neighbours. For example,

hardware based on optical elements and atomic ensembles [Sangouard11]

is very efficient at generating entanglement at high rates but

provides limited processing capabilities once the entanglement is

generated. On the other hand, nitrogen-vacancy-based platforms

[Hensen15] or trapped ion platforms [Moehring07] offer a much greater

degree of control over the qubits but have a harder time generating

entanglement at high rates.

In order to overcome the weaknesses of the different platforms,

coupling the different technologies will help to build fully

functional networks. For example, end nodes may be implemented using

technology with good qubit processing capabilities to enable complex

applications, but automated quantum nodes that serve only to "repeat"

along a linear chain, where the processing logic is much simpler, can

be implemented with technologies that sacrifice processing

capabilities for higher entanglement rates at long distances

[Askarani21].

This point is further exacerbated by the fact that quantum computers

(i.e., end nodes in a quantum network) are often based on different

hardware platforms than quantum repeaters, thus requiring a coupling

(transduction) between the two. This is especially true for quantum

computers based on superconducting technology, which are challenging

to connect to optical networks. However, even trapped ion quantum

computers, which make up a platform that has shown promise for

quantum networking, will still need to connect to other platforms

that are better at creating entanglement at high rates over long

distances (hundreds of kilometres).

Given that the most practical way of realising quantum network

connectivity is using Bell pair and entanglement-swapping repeater

technology, what sort of principles should guide us in assembling

such networks such that they are functional, robust, efficient, and,

most importantly, will work? Furthermore, how do we design networks

so that they work under the constraints imposed by the hardware

available today but do not impose unnecessary burdens on future

technology?

As quantum networking is a completely new technology that is likely

to see many iterations over its lifetime, this document must not

serve as a definitive set of rules but merely as a general set of

recommended guidelines for the first generations of quantum networks

based on principles and observations made by the community. The

benefit of having a community-built document at this early stage is

that expertise in both quantum information and network architecture

is needed in order to successfully build a quantum internet.

When outlining any set of principles, we must ask ourselves what

goals we want to achieve, as inevitably trade-offs must be made. So,

what sort of goals should drive a quantum network architecture? The

following list has been inspired by the history of computer

networking, and thus it is inevitably very similar to one that could

be produced for the classical Internet [Clark88]. However, whilst

the goals may be similar, the challenges involved are often

fundamentally different. The list will also most likely evolve with

time and the needs of its users.

1. Support distributed quantum applications.

This goal seems trivially obvious, but it makes a subtle, but

important, point that highlights a key difference between quantum

and classical networks. Ultimately, quantum data transmission is

not the goal of a quantum network -- it is only one possible

component of quantum application protocols that are more advanced

[Wehner18]. Whilst transmission certainly could be used as a

building block for all quantum applications, it is not the most

basic one possible. For example, entanglement-based QKD, the

most well-known quantum application protocol, only relies on the

stronger-than-classical correlations and inherent secrecy of

entangled Bell pairs and does not have to transmit arbitrary

quantum states [Ekert91].

The primary purpose of a quantum internet is to support

distributed quantum application protocols, and it is of utmost

importance that they can run well and efficiently. Thus, it is

important to develop performance metrics meaningful to

applications to drive the development of quantum network

protocols. For example, the Bell pair generation rate is

meaningless if one does not also consider their fidelity. It is

generally much easier to generate pairs of lower fidelity, but

quantum applications may have to make multiple reattempts or even

abort if the fidelity is too low. A review of the requirements

for different known quantum applications can be found in

[Wehner18], and an overview of use cases can be found in

[QI-Scenarios].

2. Support tomorrow's distributed quantum applications.

The only principle of the Internet that should survive

indefinitely is the principle of constant change [RFC1958].

Technical change is continuous, and the size and capabilities of

the quantum internet will change by orders of magnitude.

Therefore, it is an explicit goal that a quantum internet

architecture be able to embrace this change. We have the benefit

of having been witness to the evolution of the classical Internet

over several decades, and we have seen what worked and what did

not. It is vital for a quantum internet to avoid the need for

flag days (e.g., NCP to TCP/IP) or upgrades that take decades to

roll out (e.g., IPv4 to IPv6).

Therefore, it is important that any proposed architecture for

general-purpose quantum repeater networks can integrate new

devices and solutions as they become available. The architecture

should not be constrained due to considerations for early-stage

hardware and applications. For example, it is already possible

to run QKD efficiently on metropolitan-scale networks, and such

networks are already commercially available. However, they are

not based on quantum repeaters and thus will not be able to

easily transition to applications that are more sophisticated.

3. Support heterogeneity.

There are multiple proposals for realising practical quantum

repeater hardware, and they all have their advantages and

disadvantages. Some may offer higher Bell pair generation rates

on individual links at the cost of entanglement swap operations

that are more difficult. Other platforms may be good all around

but are more difficult to build.

In addition to physical boundaries, there may be distinctions in

how errors are managed (Section 4.4.3.3). These differences will

affect the content and semantics of messages that cross these

boundaries -- for both connection setup and real-time operation.

The optimal network configuration will likely leverage the

advantages of multiple platforms to optimise the provided

service. Therefore, it is an explicit goal to incorporate varied

hardware and technology support from the beginning.

4. Ensure security at the network level.

The question of security in quantum networks is just as critical

as it is in the classical Internet, especially since enhanced

security offered by quantum entanglement is one of the key

driving factors.

Fortunately, from an application's point of view, as long as the

underlying implementation corresponds to (or sufficiently

approximates) theoretical models of quantum cryptography, quantum

cryptographic protocols do not need the network to provide any

guarantees about the confidentiality or integrity of the

transmitted qubits or the generated entanglement (though they may

impose requirements on the classical channel, e.g., to be

authenticated [Wang21]). Instead, applications will leverage the

classical networks to establish the end-to-end security of the

results obtained from the processing of entangled qubits.

However, it is important to note that whilst classical networks

are necessary to establish these end-to-end guarantees, the

security relies on the properties of quantum entanglement. For

example, QKD uses classical information reconciliation [Tang19]

for error correction and privacy amplification [Elkouss11] for

generating the final secure key, but the raw bits that are fed

into these protocols must come from measuring entangled qubits

[Ekert91]. In another application, secure delegated quantum

computing, the client hides its computation from the server by

sending qubits to the server and then requesting (in a classical

message) that the server measure them in an encoded basis. The

client then decodes the results it receives from the server to

obtain the result of the computation [Broadbent10]. Once again,

whilst a classical network is used to achieve the goal of secure

computation, the remote computation is strictly quantum.

Nevertheless, whilst applications can ensure their own end-to-end

security, network protocols themselves should be security aware

in order to protect the network itself and limit disruption.

Whilst the applications remain secure, they are not necessarily

operational or as efficient in the presence of an attacker. For

example, if an attacker can measure every qubit between two

parties trying to establish a key using QKD, no secret key can be

generated. Security concerns in quantum networks are described

in more detail in [Satoh17] and [Satoh20].

5. Make them easy to monitor.

In order to manage, evaluate the performance of, or debug a

network, it is necessary to have the ability to monitor the

network while ensuring that there will be mechanisms in place to

protect the confidentiality and integrity of the devices

connected to it. Quantum networks bring new challenges in this

area, so it should be a goal of a quantum network architecture to

make this task easy.

The fundamental unit of quantum information, the qubit, cannot be

actively monitored, as any readout irreversibly destroys its

contents. One of the implications of this fact is that measuring

an individual pair's fidelity is impossible. Fidelity is

meaningful only as a statistical quantity that requires constant

monitoring of generated Bell pairs, achieved by sacrificing some

Bell pairs for use in tomography or other methods.

Furthermore, given one end of an entangled pair, it is impossible

to tell where the other qubit is without any additional classical

metadata. It is impossible to extract this information from the

qubits themselves. This implies that tracking entangled pairs

necessitates some exchange of classical information. This

information might include (i) a reference to the entangled pair

that allows distributed applications to coordinate actions on

qubits of the same pair and (ii) the two bits from each

entanglement swap necessary to identify the final state of the

Bell pair (Section 4.4.2).

6. Ensure availability and resilience.

Any practical and usable network, classical or quantum, must be

able to continue to operate despite losses and failures and be

robust to malicious actors trying to disable connectivity. A

difference between quantum and classical networks is that quantum

networks are composed of two types of data planes (quantum and

classical) and two types of channels (quantum and classical) that

must be considered. Therefore, availability and resilience will

most likely require a more advanced treatment than they do in

classical networks.

Note that privacy, whilst related to security, is not listed as an

explicit goal, because the privacy benefits will depend on the use

case. For example, QKD only provides increased security for the

distribution of symmetric keys [Bennett14] [Ekert91]. The handling,

manipulation, sharing, encryption, and decryption of data will remain

entirely classical, limiting the benefits to privacy that can be

gained from using a quantum network. On the other hand, there are

applications like blind quantum computation, which provides the user

with the ability to execute a quantum computation on a remote server

without the server knowing what the computation was or its input and

output [Fitzsimons17]. Therefore, privacy must be considered on a

per-application basis. An overview of quantum network use cases can

be found in [QI-Scenarios].

The principles support the goals but are not goals themselves. The

goals define what we want to build, and the principles provide a

guideline for how we might achieve this. The goals will also be the

foundation for defining any metric of success for a network

architecture, whereas the principles in themselves do not distinguish

between success and failure. For more information about design

considerations for quantum networks, see [VanMeter13.1] and

[Dahlberg19].

1. Entanglement is the fundamental service.

The key service that a quantum network provides is the

distribution of entanglement between the nodes in a network. All

distributed quantum applications are built on top of this key

resource. Applications such as clustered quantum computing,

distributed quantum computing, distributed quantum sensing

networks, and certain kinds of quantum secure networks all

consume quantum entanglement as a resource. Some applications

(e.g., QKD) simply measure the entangled qubits to obtain a

shared secret key [QKD]. Other applications (e.g., distributed

quantum computing) build abstractions and operations that are

more complex on the entangled qubits, e.g., distributed CNOT

gates [DistCNOT] or teleportation of arbitrary qubit states

[Teleportation].

A quantum network may also distribute multipartite entangled

states (entangled states of three or more qubits) [Meignant19],

which are useful for applications such as conference key

agreement [Murta20], distributed quantum computing [Cirac99],

secret sharing [Qin17], and clock synchronisation [Komar14],

though it is worth noting that multipartite entangled states can

also be constructed from multiple entangled pairs distributed

between the end nodes.

2. Bell pairs are indistinguishable.

Any two Bell pairs between the same two nodes are

indistinguishable for the purposes of an application, provided

they both satisfy its required fidelity threshold. This

observation is likely to be key in enabling a more optimal

allocation of resources in a network, e.g., for the purposes of

provisioning resources to meet application demand. However, the

qubits that make up the pair themselves are not

indistinguishable, and the two nodes operating on a pair must

coordinate to make sure they are operating on qubits that belong

to the same Bell pair.

3. Fidelity is part of the service.

In addition to being able to deliver Bell pairs to the

communication end-points, the Bell pairs must be of sufficient

fidelity. Unlike in classical networks, where most errors are

effectively eliminated before reaching the application, many

quantum applications only need imperfect entanglement to

function. However, quantum applications will generally have a

threshold for Bell pair fidelity below which they are no longer

able to operate. Different applications will have different

requirements for what fidelity they can work with. It is the

network's responsibility to balance the resource usage with

respect to the applications' requirements. It may be that it is

cheaper for the network to provide lower-fidelity pairs that are

just above the threshold required by the application than it is

to guarantee high-fidelity pairs to all applications regardless

of their requirements.

4. Time is an expensive resource.

Time is not the only resource that is in short supply

(communication qubits and memory are as well), but ultimately it

is the lifetime of quantum memories that imposes some of the most

difficult conditions for operating an extended network of quantum

nodes. Current hardware has low rates of Bell pair generation,

short memory lifetimes, and access to a limited number of

communication qubits. All these factors combined mean that even

a short waiting queue at some node could be enough for a Bell

pair to decohere or result in an end-to-end pair below an

application's fidelity threshold. Therefore, managing the idle

time of qubits holding live quantum states should be done

carefully -- ideally by minimising the idle time, but potentially

also by moving the quantum state for temporary storage to a

quantum memory with a longer lifetime.

5. Be flexible with regards to capabilities and limitations.

This goal encompasses two important points:

* First, the architecture should be able to function under the

physical constraints imposed by the current-generation

hardware. Near-future hardware will have low entanglement

generation rates, quantum memories able to hold a handful of

qubits at best, and decoherence rates that will render many

generated pairs unusable.

* Second, the architecture should not make it difficult to run

the network over any hardware that may come along in the

future. The physical capabilities of repeaters will improve,

and redeploying a technology is extremely challenging.

To conclude, we discuss a plausible quantum network architecture

inspired by MPLS. This is not an architecture proposal but rather a

thought experiment to give the reader an idea of what components are

necessary for a functional quantum network. We use classical MPLS as

a basis, as it is well known and understood in the networking

community.

Creating end-to-end Bell pairs between remote end-points is a

stateful distributed task that requires a lot of a priori

coordination. Therefore, a connection-oriented approach seems the

most natural for quantum networks. In connection-oriented quantum

networks, when two quantum application end-points wish to start

creating end-to-end Bell pairs, they must first create a Quantum

Virtual Circuit (QVC). As an analogy, in MPLS networks, end-points

must establish a Label Switched Path (LSP) before exchanging traffic.

Connection-oriented quantum networks may also support virtual

circuits with multiple end-points for creating multipartite

entanglement. As an analogy, MPLS networks have the concept of

multipoint LSPs for multicast.

When a quantum application creates a QVC, it can indicate Quality of

Service (QoS) parameters such as the required capacity in end-to-end

Bell Pairs Per Second (BPPS) and the required fidelity of the Bell

pairs. As an analogy, in MPLS networks, applications specify the

required bandwidth in Bits Per Second (BPS) and other constraints

when they create a new LSP.

Different applications will have different QoS requirements. For

example, applications such as QKD that don't need to process the

entangled qubits, and only need measure them and store the resulting

outcome, may require a large volume of entanglement but will be

tolerant of delay and jitter for individual pairs. On the other

hand, distributed/cloud quantum computing applications may need fewer

entangled pairs but instead may need all of them to be generated in

one go so that they can all be processed together before any of them

decohere.

Quantum networks need a routing function to compute the optimal path

(i.e., the best sequence of routers and links) for each new QVC. The

routing function may be centralised or distributed. In the latter

case, the quantum network needs a distributed routing protocol. As

an analogy, classical networks use routing protocols such as Open

Shortest Path First (OSPF) and Intermediate System to Intermediate

System (IS-IS). However, note that the definition of "shortest path"

/ "least cost" may be different in a quantum network to account for

its non-classical features, such as fidelity [VanMeter13.2].

Given the very scarce availability of resources in early quantum

networks, a Traffic Engineering (TE) function is likely to be

beneficial. Without TE, QVCs always use the shortest path. In this

case, the quantum network cannot guarantee that each quantum end-

point will get its Bell pairs at the required rate or fidelity. This

is analogous to "best effort" service in classical networks.

With TE, QVCs choose a path that is guaranteed to have the requested

resources (e.g., bandwidth in BPPS) available, taking into account

the capacity of the routers and links and also taking into account

the resources already consumed by other virtual circuits. As an

analogy, both OSPF and IS-IS have TE extensions to keep track of used

and available resources and can use Constrained Shortest Path First

(CSPF) to take resource availability and other constraints into

account when computing the optimal path.

The use of TE implies the use of Call Admission Control (CAC): the

network denies any virtual circuits for which it cannot guarantee the

requested quality of service a priori. Alternatively, the network

preempts lower-priority circuits to make room for a new circuit.

Quantum networks need a signalling function: once the path for a QVC

has been computed, signalling is used to install the "forwarding

rules" into the data plane of each quantum router on the path. The

signalling may be distributed, analogous to the Resource Reservation

Protocol (RSVP) in MPLS. Or, the signalling may be centralised,

similar to OpenFlow.

Quantum networks need an abstraction of the hardware for specifying

the forwarding rules. This allows us to decouple the control plane

(routing and signalling) from the data plane (actual creation of Bell

pairs). The forwarding rules are specified using abstract building

blocks such as "creating local Bell pairs", "swapping Bell pairs", or

"distillation of Bell pairs". As an analogy, classical networks use

abstractions that are based on match conditions (e.g., looking up

header fields in tables) and actions (e.g., modifying fields or

forwarding a packet to a specific interface). The data plane

abstractions in quantum networks will be very different from those in

classical networks due to the fundamental differences in technology

and the stateful nature of quantum networks. In fact, choosing the

right abstractions will be one of the biggest challenges when

designing interoperable quantum network protocols.

In quantum networks, control plane traffic (routing and signalling

messages) is exchanged over a classical channel, whereas data plane

traffic (the actual Bell pair qubits) is exchanged over a separate

quantum channel. This is in contrast to most classical networks,

where control plane traffic and data plane traffic share the same

channel and where a single packet contains both user fields and

header fields. There is, however, a classical analogy to the way

quantum networks work: generalised MPLS (GMPLS) networks use separate

channels for control plane traffic and data plane traffic.

Furthermore, GMPLS networks support data planes where there is no

such thing as data plane headers (e.g., Dense Wavelength Division

Multiplexing (DWDM) or Time-Division Multiplexing (TDM) networks).

Security is listed as an explicit goal for the architecture; this

issue is addressed in Section 6.1. However, as this is an

Informational document, it does not propose any concrete mechanisms

to achieve these goals.

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The authors want to thank Carlo Delle Donne, Matthew Skrzypczyk, Axel

Dahlberg, Mathias van den Bossche, Patrick Gelard, Chonggang Wang,

Scott Fluhrer, Joey Salazar, Joseph Touch, and the rest of the QIRG

community as a whole for their very useful reviews and comments on

this document.

WK and SW acknowledge funding received from the EU Flagship on

Quantum Technologies, Quantum Internet Alliance (No. 820445).

rdv acknowledges support by the Air Force Office of Scientific

Research under award number FA2386-19-1-4038.

Wojciech Kozlowski

QuTech

Building 22

Lorentzweg 1

2628 CJ Delft

Netherlands

Email: w.kozlowski@tudelft.nl

Stephanie Wehner

QuTech

Building 22

Lorentzweg 1

2628 CJ Delft

Netherlands

Email: s.d.c.wehner@tudelft.nl

Rodney Van Meter

Keio University

5322 Endo, Fujisawa, Kanagawa

252-0882

Japan

Email: rdv@sfc.wide.ad.jp

Bruno Rijsman

Individual

Email: brunorijsman@gmail.com

Angela Sara Cacciapuoti

University of Naples Federico II

Department of Electrical Engineering and Information Technologies

Claudio 21

80125 Naples

Italy

Email: angelasara.cacciapuoti@unina.it

Marcello Caleffi

University of Naples Federico II

Department of Electrical Engineering and Information Technologies

Claudio 21

80125 Naples

Italy

Email: marcello.caleffi@unina.it

Shota Nagayama

Mercari, Inc.

Roppongi Hills Mori Tower 18F

6-10-1 Roppongi, Minato-ku, Tokyo

106-6118

Japan