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Quantum Internet Research Group                             W. Kozlowski
Internet-Draft                                                 S. Wehner
Intended status: Informational                                    QuTech
Expires: January 13, 2021                                   R. Van Meter
                                                         Keio University
                                                              B. Rijsman
                                                              Individual
                                                       A. S. Cacciapuoti
                                                              M. Caleffi
                                        University of Naples Federico II
                                                             S. Nagayama
                                                           Mercari, Inc.
                                                           July 12, 2020


            Architectural Principles for a Quantum Internet
                     draft-irtf-qirg-principles-04

Abstract

   The vision of a quantum internet is to fundamentally enhance 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 as the physical nature of the communication
   is fundamentally different.  The first realisations of quantum
   networks are imminent, but there is no practical proposal for how to
   organise, utilise, and manage such networks.  In this memo, 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, but also to provide a
   foundation for discussion between physicists and network specialists.

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at https://datatracker.ietf.org/drafts/current/.

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on January 13, 2021.



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Copyright Notice

   Copyright (c) 2020 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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   described in the Simplified BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
   2.  Quantum information . . . . . . . . . . . . . . . . . . . . .   4
     2.1.  Qubit . . . . . . . . . . . . . . . . . . . . . . . . . .   4
     2.2.  Multiple qubits . . . . . . . . . . . . . . . . . . . . .   5
   3.  Entanglement as the fundamental resource  . . . . . . . . . .   6
   4.  Achieving quantum connectivity  . . . . . . . . . . . . . . .   7
     4.1.  Challenges  . . . . . . . . . . . . . . . . . . . . . . .   8
       4.1.1.  The measurement problem . . . . . . . . . . . . . . .   8
       4.1.2.  No-cloning theorem  . . . . . . . . . . . . . . . . .   8
       4.1.3.  Fidelity  . . . . . . . . . . . . . . . . . . . . . .   8
       4.1.4.  Inadequacy of direct transmission . . . . . . . . . .   9
     4.2.  Bell pairs  . . . . . . . . . . . . . . . . . . . . . . .   9
     4.3.  Teleportation . . . . . . . . . . . . . . . . . . . . . .  10
     4.4.  The life cycle of entanglement  . . . . . . . . . . . . .  11
       4.4.1.  Elementary link generation  . . . . . . . . . . . . .  11
       4.4.2.  Entanglement swapping . . . . . . . . . . . . . . . .  12
       4.4.3.  Error Management  . . . . . . . . . . . . . . . . . .  13
       4.4.4.  Delivery  . . . . . . . . . . . . . . . . . . . . . .  16
   5.  Architecture of a quantum internet  . . . . . . . . . . . . .  16
     5.1.  Challenges  . . . . . . . . . . . . . . . . . . . . . . .  16
     5.2.  Classical communication . . . . . . . . . . . . . . . . .  18
     5.3.  Abstract model of the network . . . . . . . . . . . . . .  19
       5.3.1.  Elements of a quantum network . . . . . . . . . . . .  19
       5.3.2.  Putting it all together . . . . . . . . . . . . . . .  20
     5.4.  Network boundaries  . . . . . . . . . . . . . . . . . . .  21
       5.4.1.  Boundaries between different physical architectures .  21
       5.4.2.  Boundaries between different administrative regions .  21
       5.4.3.  Boundaries between different error management schemes  22
     5.5.  Physical constraints  . . . . . . . . . . . . . . . . . .  22
       5.5.1.  Memory lifetimes  . . . . . . . . . . . . . . . . . .  22
       5.5.2.  Rates . . . . . . . . . . . . . . . . . . . . . . . .  22



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       5.5.3.  Communication qubits  . . . . . . . . . . . . . . . .  23
       5.5.4.  Homogeneity . . . . . . . . . . . . . . . . . . . . .  23
   6.  Architectural principles  . . . . . . . . . . . . . . . . . .  23
     6.1.  Goals of a quantum internet . . . . . . . . . . . . . . .  24
     6.2.  The principles of a quantum internet  . . . . . . . . . .  26
   7.  Comparison with classical networks  . . . . . . . . . . . . .  28
   8.  Security Considerations . . . . . . . . . . . . . . . . . . .  30
   9.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  30
   10. Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  30
   11. Informative References  . . . . . . . . . . . . . . . . . . .  31
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  33

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.  Depending on the stage of a quantum network [8] such
   devices may be 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 form an overall
   hybrid classical quantum network supporting new capabilities which
   are otherwise impossible to realise.

   This new networking paradigm offers promise for a range of new
   applications such as secure communications [3] [4], distributed
   quantum computation [5], or quantum-enhanced measurement networks
   [6].  The field of quantum communication has been a subject of active
   research for many years and the most well-known application of
   quantum communication, quantum key distribution (QKD) for secure
   communications, has already been deployed at short (roughly 100km)
   distances.

   Fully quantum networks capable of transmitting and managing entangled
   quantum states in order to send, receive, and manipulate distributed
   quantum information are now imminent [7] [8].  Whilst a lot of effort
   has gone into physically realising and connecting such devices, and
   making improvements to their speed and error tolerance, there are no
   worked out proposals for how to run these networks.  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 itself at a level below
   convential assembly language, where no common interfaces yet exist.
   Furthermore, whilst physical mechanisms for transmitting quantum




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   states exist, there are no robust protocols for managing such
   transmissions.

2.  Quantum information

   In order to understand the framework for quantum networking, a basic
   understanding of quantum information is necessary.  The following
   sections aim to introduce the bare minimum 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 to e.g. [15] [16] for an in-depth introduction to
   quantum information.

2.1.  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, a qubit, exists over the same
   binary space, but unlike the classical bit, it can exist in a
   superposition of the two possibilities:

   a |0> + b |1>,

   where |X> is Dirac's ket notation for a quantum state, 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 is not deterministic, but it can be
   determined from the readout of the measurement, a classical bit, 0 or
   1 respectively.  The probability of measuring the state in the |0>
   state is |a|^2 and 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
   it is a fundamental feature of a quantum mechanical system [9].

   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>.




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2.2.  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).  Let us now consider the two-
   qubit controlled-NOT, or CNOT, gate.  The CNOT gate takes as input
   two qubits, a control and 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 |
                               +----+-----+

   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).





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   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 and the behaviour of either qubit cannot be fully
   described without accounting for the other qubit.  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.

   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, blind quantum
   computation, or distributed quantum computation.

   Entanglement has two very special features from which one can derive
   some intuition about the types of applications enabled by a quantum
   network.



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   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 more complicated measurement
   schemes 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 any other system to have any
   share of this entanglement.  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.

   More complex services and applications can be built on top of
   entangled states distributed by the network, see e.g. [8]>

4.  Achieving quantum connectivity

   This section explains the meaning of quantum connectivity and the
   necessary physical processes at an abstract level.






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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 the question if we can simply copy a qubit without looking
   at it.  Unfortunately, this is fundamentally not possible in quantum
   mechanics.

   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 is more involved.



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   To describe the quality of a quantum state, a physical quantity
   called fidelity is used.  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 one state will pass a test
   to identify as the other.  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 by
   employing quantum error detection and correction mechanisms.

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 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 [10].  However, quantum error correction
   makes very high demands on both resources (physical qubits needed)
   and their initial fidelity.  Implementation is very challenging and
   quantum error correction is not expected to be used until later
   generations of quantum networks.

   An 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[18].

4.2.  Bell pairs

   Bell pair states are the entangled two-qubit states:

   |00> + |11>,
   |00> - |11>,
   |01> + |10>,
   |01> - |10>,



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   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 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 discussed in a later
   section) 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, less entangled states 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.  Quantum state teleportation consumes an unknown
   quantum 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 read out 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 measurements 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 quantum state that we wanted to transmit.





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   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 and quantum data planes is
   that a classical one carries user data, but a quantum data plate
   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 facilitated the problem, 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, called 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 cannot be stored, 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 [19]:

   o  "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




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      successful entanglement generation via a message exchange over the
      classical channel.

   o  "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.

   o  "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 two 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 10s of
   kms in optical fibre or 1000 kms 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.

   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 that it is connected to in order to
   produce a new entangled pair between the two remote ends.  This
   process is known as entanglement swapping.  Pictorially it can be
   represented as follows:







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   +---------+      +---------+      +---------+
   |    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 which result 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 read out 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 [18] and we will use the same
   terminology in this memo.

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).



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   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 quantum error correction, but distributed
   protocols incur round-trip delays due to classical communication
   [17].

4.4.3.2.  Quantum Error Correction

   Just like classical error correction, quantum error correction (QEC)
   encodes logical qubits using several physical (raw) qubits to protect
   them from errors described in Section 4.1.3.  Furthermore, similarly
   to its classical counterpart, QEC can not only correct state errors
   but also account for lost qubits.  Additionally, if all physical
   qubits which 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.

   One big difference from classical error correction is the code-rate.
   QEC encodes a single logical qubit using many physical qubits.

4.4.3.3.  Error management schemes

   Quantum networks have been categorized into three "generations" based
   on the error management scheme they employ[10].  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 more advanced technologies.  Which generation
   is used depends on the hardware platform and network design choices.

   Table Table 1 summarises the generations.










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   +-----------+-----------------+------------------------+------------+
   |           |      First      |   Second generation    |   Third    |
   |           |    generation   |                        | generation |
   +-----------+-----------------+------------------------+------------+
   |    Loss   |     Heralded    | Heralded entanglement  |  Quantum   |
   | tolerance |   entanglement  |    generation (bi-     |   Error    |
   |           | generation (bi- | directional classical  | Correction |
   |           |   directional   |       signaling)       |    (no     |
   |           |    classical    |                        | classical  |
   |           |    signaling)   |                        | signaling) |
   |           |                 |                        |            |
   |   Error   |   Entanglement  |      Entanglement      |  Quantum   |
   | tolerance |   distillation  |   distillation (uni-   |   Error    |
   |           | (bi-directional | directional classical  | Correction |
   |           |    classical    |     signaling) or      |    (no     |
   |           |    signaling)   |     Quantum Error      | classical  |
   |           |                 |     Correction (no     | signaling) |
   |           |                 |  classical signaling)  |            |
   +-----------+-----------------+------------------------+------------+

               Table 1: Classical signaling 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 and
   incurs round-trip delays described in Section 4.4.3.1, hence they
   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 a
   heralding signal is received.  As described in Section 4.4.3.2, QEC
   can be applied to complement lost qubits eliminating the need for re-
   attempts.  Furthermore, since the correction procedure is composed of
   local operations, it does not require a heralding signal.  However,
   it is feasible only when the photon loss rate is less than 0.5.

   Error tolerance is about tolerating quantum state errors.
   Entanglement distillation is the easiest mechanism for improved error
   tolerance to implement, but it incurs round-trip delays due the
   requirement for bi-directional 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 uni-directional classical signalling.



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   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 using only small, shallow
       quantum circuits at each node.

   2.  Second generation quantum networks are empowered by QEC codes for
       error tolerance.  At first, QEC will be applied to entanglement
       distillation only which requires uni-directional classical
       signalling.  Later, QEC codes will be used to create logical Bell
       pairs which 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.

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 memo.  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 building
   quantum networks.  Here, we only describe the fundamental
   differences.  Technological limitations are described later.

   1.  Bell pairs are not equivalent to payload carrying packets.





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       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 which 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.

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

       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 an 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, 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.
       This distinction makes control algorithms and optimisation of
       quantum networks different from classical ones.  Note that third
       generation quantum networks, as described in Section 4.4.1, 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.




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       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 is 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 looks up 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 memo we have already covered two different roles that
   classical communication must perform:

   o  communicate classical bits of information as part of distributed
      protocols such as entanglement swapping and teleportation,

   o  communicate control information within a network, including both
      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 limts).  Therefore, quantum routers will need to manage two
   data planes in parallel, a classical one and a quantum one.
   Additionally, a node must be able to correlate information between



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   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.  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:

   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:

   o  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.

   o  Automated quantum nodes - An automated quantum node is a data
      plane only quantum repeater that does not participate in network
      management.  Since the no-cloning theorem precludes the use of
      amplification, long-range links will be established by chaining
      multiple such automated nodes together.

   o  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.

   o  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.




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   Additionally, we need to identify two kinds of links that will be
   used in a quantum network:

   o  Quantum links - A quantum link is a link which can be used to
      generate an entangled pair between two directly connected quantum
      repeaters.  It may include a dedicated classical channel that is
      to be used solely for the purpose of coordinating the entanglement
      generation on this quantum link.

   o  Classical links - A classical link is a link between any node in
      the network that is capable of carrying classical network traffic.

5.3.2.  Putting it all together

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

   | App |-------------------CC-------------------| App |
      ||                                            ||
    ------                 ------                 ------
   |  EN  |----QC & CC----|  QR  |----QC & CC----|  EN  |
    ------                 ------                 ------

   App - user-level application
   QR - quantum repeater
   EN - end-node
   QC - quantum channel
   CC - classical channel

   An application running on two end-nodes attached to a network will at
   some point need the network to generate entangled pairs for its use.
   This will require negotiation between the end-nodes, because they
   must both open a communication end-point (a quantum socket) which the
   network can use to identify the two ends of the connection.  The two
   end-nodes use the classical connectivity 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 communication channels 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 and thus beyond the scope of this memo.

   During or after the distribution of control information, the network
   performs the necessary quantum operations such as generating
   entanglement over individual links, performing entanglement swaps,
   and further signalling to transmit the swap outcomes and other
   control information.  Since none of the entangled pairs carry any



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   user data, some of these operations can be performed before the
   request is received in anticipation of the demand.

   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 end node.

5.4.  Network boundaries

   Just like classical networks, various boundaries will exist in
   quantum networks.

5.4.1.  Boundaries between different physical architectures

   There are many different physical architectures for implementing
   quantum repeater technology.  The different technologies differ in
   how they store and manipulate qubits in memory and how they generate
   entanglement across a link with their neighbours.  Different
   architectures come with different trade-offs and thus a functional
   network will likely consist of a mixture of different types of
   quantum repeaters.

   For example, architectures based on optical elements and atomic
   ensembles are very efficient at generating entanglement, but provide
   little control over the qubits once the pair is generated.  On the
   other hand, nitrogen-vacancy architectures offer a much greater
   degree of control over qubits, but have a harder time generating the
   entanglement across a link.

   It is an open research question where exactly the boundary will lie.
   It could be that a single quantum repeater node provides some
   backplane connection between the architectures, but it also could be
   that special quantum links delineate the boundary.

5.4.2.  Boundaries between different administrative regions

   Just like in classical networks, multiple quantum networks will
   connect into a global quantum internet.  This necessarily implies the
   existence of borders between different administrative regions.  How
   these boundaries will be handled is also an open question and thus
   beyond the scope of this memo.






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5.4.3.  Boundaries between different error management schemes

   Not only are there physical differences and administrative
   boundaries, but there are important distinctions in how errors will
   be managed, as described in Section 4.4.3.3, which affects the
   content and semantics of messages that must cross those boundaries --
   both for connection setup and real-time operation.  How to
   interconnect those schemes is also an open research question.

5.5.  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 artefacts of the early stages of a new technology.  Here, we
   consider a highly abstract scenario and refer to [8] for pointers to
   the physics literature.

5.5.1.  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 currently are on the order of seconds.
   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.

5.5.2.  Rates

   Entanglement generation on a link between two connected nodes is not
   a very efficient process and it requires many attempts to succeed.  A
   fast repetition rate for Bell pair generation is achievable, but only
   a small fraction will succeed.  Currently, the highest achievable
   rates of success between nodes capable of storing the resulting
   qubits are on the order of 10 Hz.  Combined with short memory




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   lifetimes this leads to very tight timing windows to build up
   network-wide connectivity.

5.5.3.  Communication qubits

   Most physical architectures capable of storing qubits are only able
   to generate entanglement using only a subset of its available qubits
   called communication qubits.  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.

5.5.4.  Homogeneity

   Currently all hardware implementations are homogeneous and they do
   not interface with each other.  In general, it is very challenging to
   combine different quantum information processing technologies at
   present.  Coupling different technologies with each other is of great
   interest as it may help overcome the weaknesses of the different
   implementations, but this may take a long time to be realised with
   high reliability and thus is not a near-term goal.

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, they 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 this is a completely new technology that is likely to see many
   iterations over its lifetime, this memo 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.








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6.1.  Goals of a quantum internet

   When outlining any set of principles we must ask ourselves what goals
   do 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 [21].  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 makes a subtle, but
       important point which 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 more advanced quantum application protocols.  Whilst
       transmission certainly could be used as a building block for all
       quantum applications, it is not the most basic one possible.  For
       example, 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 transmit
       arbitrary quantum states[4].

       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
       application 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 re-attempts or
       even abort if the fidelity is too low.  A review of the
       requirements for different known quantum applications can be
       found in [8] and an overview of use-cases can be found in [2].

   2.  Support tomorrow's distributed quantum applications

       The only principle of the Internet that should survive
       indefinitely is the principle of constant change [1].  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



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       and 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.  It 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 scales 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 more
       sophisticated applications.

   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 more difficult entanglement
       swap operations.  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 difference will
       affect the content and semantics of messages that cross these
       boundaries -- both for 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.

       It turns out that 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.  Instead, applications, such as QKD,
       establish such guarantees in an end-to-end fashion using the
       classical network in conjunction with the quantum one.




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       Nevertheless, whilst applications can ensure their own secure
       operation, 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.
       Security concerns in quantum networks are described in more
       detail in [13] [12].

   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.  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 which requires the
       constant monitoring and the sacrifice of generated Bell pairs for
       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
       information.  It is impossible to extract this information from
       the qubits themselves.  This implies that tracking entangled
       pairs necessitates some exchange of classical information.

   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.  What
       differs in quantum networks as compared to classical networks in
       this regard is that we now have two data planes and two types of
       channels to worry about: a quantum and a classical one.
       Therefore, availability and resilience will most likely require a
       more advanced treatment than they do in classical networks.

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 in 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



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   between success and failure.  For more information about design
   considerations for quantum networks see [11] [14] .

   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.  Bell pairs are the minimal entanglement building block
       that is sufficient to develop these applications.  However, a
       quantum network may also distribute multipartite entangled states
       (entangled states of three or more qubits)[20] as this may be
       more efficient under certain circumstances.

   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 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 part of the service





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       With the current technology, time is the most expensive resource.
       It is not the only resource that is in short supply (memory, and
       communication qubits are as well), but ultimately it is the
       lifetime of quantum memories that imposes 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 the Bell Pairs to
       decohere.  It is vital that quantum networks deliver entanglement
       in a timely manner.  The meaning of timeliness will depend on the
       needs of the application (how long does it need to store the Bell
       pair in its own memory and/or what operations it wants to apply
       to it).

   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, it 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.  Comparison with classical networks

   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 this section, we discuss a
   plausible quantum network architecture inspired by MPLS.  This is not
   an architecture proposal, but 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.

   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




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   multipartite entanglement.  As an analogy, MPLS networks have the
   concept of multi-point LSPs for multicast.

   When a quantum application creates a quantum virtual circuit, 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.

   Quantum networks need a routing function to compute the optimal path
   (i.e. the best sequence of routers and links) for each new quantum
   virtual circuit.  The routing function may be centralized 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).

   Given the very scarce availability of resources in early quantum
   networks, a traffic engineering function is likely to be beneficial.
   Without traffic engineering, quantum virtual circuits 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 traffic engineering, quantum virtual circuits 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 taking into account the resources already consumed by other
   virtual circuits.  As an analogy, both OSPF and IS-IS have traffic
   engineering (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 traffic engineering 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.  Or
   alternatively, the network pre-empts lower priority circuits to make
   room for the new one.

   Quantum networks need a signaling function: once the path for a
   quantum virtual circuit has been computed, signaling is used to
   install the "forwarding rules" into the data plane of each quantum
   router on the path.  The signaling may be distributed, analogous to
   the resource reservation protocol (RSVP) in MPLS.  Or the signaling
   may be centralized, similar to OpenFlow.



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   Quantum networks need an abstraction of the hardware for specifying
   the forwarding rules.  This allows us to de-couple the control plane
   (routing and signaling) 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",
   "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 signaling
   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.  Generalized 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.  DWDM or TDM networks).

8.  Security Considerations

   Even though no user data enters a quantum network, security is listed
   as an explicit goal for the architecture and this issue is addressed
   in the section on goals.  However, as this is an informational memo
   it does not propose any concrete mechanisms to achieve these goals.

9.  IANA Considerations

   This memo includes no request to IANA.

10.  Acknowledgements

   The authors want to thank Carlo Delle Donne, Matthew Skrzypczyk, Axel
   Dahlberg, Mathias van den Bossche, Patrick Gelard, Chonggang Wang,
   Scott Fluhrer, and the rest of the QIRG community as a whole for
   their very useful reviews and comments to the document.







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11.  Informative References

   [1]        Carpenter, B., Ed., "Architectural Principles of the
              Internet", RFC 1958, DOI 10.17487/RFC1958, June 1996,
              <https://www.rfc-editor.org/info/rfc1958>.

   [2]        Wang, C., Rahman, A., Li, R., and M. Aelmans,
              "Applications and Use Cases for the Quantum Internet",
              draft-irtf-qirg-quantum-internet-use-cases-01 (work in
              progress), July 2020.

   [3]        Bennett, C. and G. Brassard, "Quantum cryptography: Public
              key distribution and coin tossing", Theoretical Computer
              Science 560, 7-11, 2014,
              <http://www.sciepub.com/reference/53249>.

   [4]        Ekert, A., "Quantum cryptography based on Bell's theorem",
              Phys. Rev. Lett. Vol. 67, Iss. 6, 1991,
              <https://journals.aps.org/prl/abstract/10.1103/
              PhysRevLett.67.661>.

   [5]        Crepeau, C., Gottesman, D., and A. Smith, "Secure multi-
              party quantum computation. Proceedings of Symposium on
              Theory of Computing", Proceedings of Symposium on Theory
              of Computing , 2002,
              <https://arxiv.org/abs/quant-ph/0206138>.

   [6]        Giovanetti, V., Lloyd, S., and L. Maccone, "Quantum-
              enhanced measurements: beating the standard quantum
              limit", Science 306(5700), 1330-1336, 2004,
              <https://arxiv.org/abs/quant-ph/0412078>.

   [7]        Castelvecchi, D., "The Quantum Internet has arrived (and
              it hasn't)", Nature 554, 289-292, 2018,
              <https://www.nature.com/articles/d41586-018-01835-3>.

   [8]        Wehner, S., Elkouss, D., and R. Hanson, "Quantum internet:
              A vision for the road ahead", Science 362, 6412, 2018,
              <http://science.sciencemag.org/content/362/6412/
              eaam9288.full>.

   [9]        Aspect, A., Grangier, P., and G. Roger, "Experimental
              Tests of Realistic Local Theories via Bell's Theorem",
              Phys. Rev. Lett. 47 (7): 460-463, 1981,
              <https://journals.aps.org/prl/abstract/10.1103/
              PhysRevLett.47.460>.





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   [10]       Muralidharan, S., Li, L., Kim, J., Lutkenhaus, N., Lukin,
              M., and L. Jiang, "Optimal architectures for long distance
              quantum communication", Nat. Sci. Rep. 6, 20463, 2016,
              <https://www.nature.com/articles/srep20463>.

   [11]       Van Meter, R. and J. Touch, "Designing quantum repeater
              networks", IEEE Communications Magazine 51, 64-71, 2013,
              <https://ieeexplore.ieee.org/document/6576340>.

   [12]       Satoh, T., Nagayama, S., Suzuki, S., Matsuo, T., and R.
              Van Meter, "Attacking the Quantum Internet",
              arXiv 2005.04617, 2020,
              <https://arxiv.org/abs/2005.04617>.

   [13]       Satoh, T., Nagayama, S., and R. Van Meter, "The Network
              Impact of Hijacking a Quantum Repeater", arXiv 1701.04587,
              2017, <https://arxiv.org/abs/1701.04587>.

   [14]       Dahlberg, A., Skrzypczyk, M., Coopmans, T., Wubben, L.,
              Rozpedek, F., Pompili, M., Stolk, A., Pawelczak, P.,
              Knegjens, R., de Oliveira Filho, J., Hanson, R., and S.
              Wehner, "A Link Layer Protocol for Quantum Networks",
              arXiv 1903.09778, 2019,
              <https://arxiv.org/abs/1903.09778>.

   [15]       Sutor, R., "Dancing with Qubits", Packt Publishing , 2019.

   [16]       Nielsen, M. and I. Chuang, "Quantum Computation and
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   [17]       Bennett, C., DiVincenzo, D., Smolin, J., and W. Wootters,
              "Mixed State Entanglement and Quantum Error Correction",
              Phys. Rev. A Vol. 54, Iss. 5, 1996,
              <https://arxiv.org/abs/quant-ph/9604024>.

   [18]       Briegel, H., Dur, W., Cirac, J., and P. Zoller, "Quantum
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              Quantum Communication", Phys. Rev. Lett. Vol. 81, Num. 26,
              1998, <https://arxiv.org/abs/quant-ph/9803056>.

   [19]       Cacciapuoti, A., Caleffi, M., Van Meter, R., and L. Hanzo,
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              <https://arxiv.org/abs/1907.06197>.







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   [20]       Meignant, C., Markham, D., and F. Grosshans, "Distributing
              graph states over arbitrary quantum networks", Phys. Rev.
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Authors' Addresses

   Wojciech Kozlowski
   QuTech
   Building 22
   Lorentzweg 1
   Delft  2628 CJ
   Netherlands

   Email: w.kozlowski@tudelft.nl


   Stephanie Wehner
   QuTech
   Building 22
   Lorentzweg 1
   Delft  2628 CJ
   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







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   Angela Sara Cacciapuoti
   University of Naples Federico II
   Department of Electrical Engineering and Information Technologies
   Claudio 21
   Naples  80125
   Italy

   Email: angelasara.cacciapuoti@unina.it


   Marcello Caleffi
   University of Naples Federico II
   Department of Electrical Engineering and Information Technologies
   Claudio 21
   Naples  80125
   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























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