



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

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.

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   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
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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
   Email: shota.nagayama@mercari.com
