draft-irtf-qirg-principles-00.txt

Quantum Internet Research Group                             W. Kozlowski
Internet-Draft                                                 S. Wehner
Intended status: Informational                                    QuTech
Expires: October 11, 2019                                  April 9, 2019


            Architectural Principles for a Quantum Internet
                     draft-irtf-qirg-principles-00

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 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

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   This Internet-Draft will expire on October 11, 2019.

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   publication of this document.  Please review these documents
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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Model of computation  . . . . . . . . . . . . . . . . . . . .   3
     2.1.  Qubit . . . . . . . . . . . . . . . . . . . . . . . . . .   3
     2.2.  Multiple qubits . . . . . . . . . . . . . . . . . . . . .   4
   3.  Entanglement as the fundamental service . . . . . . . . . . .   5
   4.  Achieving quantum connectivity  . . . . . . . . . . . . . . .   7
     4.1.  No-cloning theorem  . . . . . . . . . . . . . . . . . . .   7
     4.2.  Direct transmission . . . . . . . . . . . . . . . . . . .   8
     4.3.  Bell pairs and entanglement swapping  . . . . . . . . . .   8
       4.3.1.  Bell Pairs  . . . . . . . . . . . . . . . . . . . . .   8
       4.3.2.  Teleportation . . . . . . . . . . . . . . . . . . . .   9
       4.3.3.  Bell Pair links and entanglement swapping . . . . . .   9
       4.3.4.  Distillation  . . . . . . . . . . . . . . . . . . . .  10
     4.4.  Direct transmission vs. swapping  . . . . . . . . . . . .  10
   5.  Architecture of a quantum internet  . . . . . . . . . . . . .  11
     5.1.  Model of a quantum network  . . . . . . . . . . . . . . .  11
     5.2.  Physical constraints  . . . . . . . . . . . . . . . . . .  12
       5.2.1.  Fidelity  . . . . . . . . . . . . . . . . . . . . . .  12
       5.2.2.  Memory lifetimes  . . . . . . . . . . . . . . . . . .  12
       5.2.3.  Rates . . . . . . . . . . . . . . . . . . . . . . . .  13
       5.2.4.  Communication qubit . . . . . . . . . . . . . . . . .  13
       5.2.5.  Homogeneity . . . . . . . . . . . . . . . . . . . . .  13
     5.3.  Architectural principles  . . . . . . . . . . . . . . . .  14
       5.3.1.  Goals of a quantum internet . . . . . . . . . . . . .  14
       5.3.2.  The principles of a quantum internet  . . . . . . . .  16
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .  19
   7.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  19
   8.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  19
   9.  Informative References  . . . . . . . . . . . . . . . . . . .  20
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  21

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 classical networks.
   Depending on the stage of a quantum network [5] such devices may be
   simple photonic devices capable of preparing and measuring only one



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   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 [1],
   distributed quantum computation [2], or quantum sensor networks [3].
   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 [4] [5].  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 what is even
   lower than assembly level where no common interfaces yet exist.
   Furthermore, whilst physical mechanisms for forwarding quantum states
   exist, there are no robust protocols for managing such transmissions.

2.  Model of computation

   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 be 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. [11] 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 so-
   called superposition of the two possibilities:

   a |0> + b |1>,




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   where |X> denotes 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.  This randomness is not due to our
   ignorance of the underlying mechanisms, but rather it is a
   fundamental feature of a quantum mechanical system [6].

   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>.

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:




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   (|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 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 ensemble 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 and their behaviour 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 if the
   same measurement is to be repeated, the entangled state must be
   prepared again.

3.  Entanglement as the fundamental service

   Entanglement is the fundamental building block of quantum networks.
   To see this, consider the state from the previous section:




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   (|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 algorithms 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.

   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 any 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,
   than 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.





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   It is impossible to entangle two qubits without ever having them
   directly interact with each other (e.g. by performing a local two-
   qubit gate, such as the CNOT).  A local - or mediated - interaction
   is necessary to create entanglement and thus such states cannot be
   created between two quantum nodes that cannot transmit quantum states
   to each other.  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 computer that is able only to communicate classically with
   another quantum computer is not a member of a quantum network.

   This is a crucial difference between classical and quantum networks.
   Classical applications transmit data over the network to synchronise
   distributed state.  Quantum network applications obtain distributed
   states, synchronised at the physical level via entanglement, from the
   network to perform quantum algorithms.

   More complex services and applications can be built on top of
   entangled states distributed by the network, see e.g. [5]>

4.  Achieving quantum connectivity

4.1.  No-cloning theorem

   To build a network we must first physically connect all the nodes
   with quantum channels that enable them to distribute the
   entanglement.  Unfortunately, our ability to transfer quantum states
   is complicated by the no-cloning theorem.

   The no-cloning theorem states that it is impossible to create an
   identical copy of an arbitrary unknown quantum state.  Since
   performing a measurement on a quantum state destroys its
   superposition, there is no practical way of learning the exact state
   of a qubit in an unknown state.  Therefore, it is 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 a quantum network is a challenging
   endeavour and its architecture must at its core address this very
   issue.








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4.2.  Direct transmission

   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 error correction
   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 [7].  However,
   even in the most optimistic scenarios the hardware requirements to
   fault-tolerantly transmit a single qubit are far beyond near-term
   capabilities.  Nevertheless, due to the promise of fault-tolerance
   and its favourable poly-logarithmic scaling with distance, this may
   eventually become a desirable method for entanglement distribution.

4.3.  Bell pairs and entanglement swapping

4.3.1.  Bell Pairs

   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.  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 state 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.  That is, either of
   the nodes that hold the two qubits of the Bell Pair can apply a
   series of single qubit gates to just their qubit in order to
   transform the ensemble 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) 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



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   constraints on distributed quantum algorithms.  This makes Bell Pairs
   particularly useful as a generic building block for distributed
   quantum applications.

4.3.2.  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, a Bell 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 Bell Pair
   and performs a 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 operations on its end of the Bell Pair,
   which results in a clone of the unknown quantum state of the
   transmission qubit.

   The unknown quantum state that was transmitted never entered the
   network itself.  Therefore, the network needs to only be able to
   reliably produce Bell Pairs between any two nodes in the network.

4.3.3.  Bell Pair links and entanglement swapping

   Reducing the problem to one of generating a Bell Pair state has
   facilitated the problem, but it has not solved it.

   The technology to generate a Bell Pair between two directly connected
   quantum nodes, store the qubits, and perform teleportation, already
   exists and has been demonstrated in laboratory conditions [8].
   Interestingly, neither of the two qubits of the pair need to be
   transmitted any further.

   A Bell Pair between any two nodes in the network can be constructed
   from Bell Pairs generated along each individual link on the path
   between the two end-points.  Each node along the path can consume the
   two Bell Pairs on the two links that it is connected to in order to
   produce a new Bell Pair between the two far ends.  This process is
   known as entanglement swapping.  Pictorially it can be represented as
   follows:



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    x~~~~~~~~~~~~~x x~~~~~~~~~~~~~x
   [ ]-----------[   ]-----------[ ]

   where x~~x denotes a Bell Pair with individual qubits represented by
   x, -- denotes a quantum link, and [ ] denotes a node.  The diagram
   above represents the situation after the middle node has generated a
   Bell Pair with two of its directly connected neighbours.  Now, the
   middle node performs an entanglement swap operation (the exact
   details of the mechanism are beyond the scope of this memo).  This
   operation consumes the two Bell Pairs and produces a new Bell Pair
   between the two far ends of this three-node network as follows:

    x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x
   [ ]-----------[   ]-----------[ ]

   The outcome is guaranteed to be a Bell Pair between the two end
   nodes, but which of the four possible Bell Pairs is produced is not
   deterministic.  However, the middle node will know which one was
   produced as the entanglement swap is a measurement operation that
   yields two classical bits.  The final state can be inferred from this
   two-bit readout.  Therefore, the middle node needs only to
   communicate the outcome over a classical channel to one or both ends
   who can apply a correction to transform the pair into any of its
   other forms (if so desired).

4.3.4.  Distillation

   Neither the Bell Pair or the swapping operations are lossless
   operations.  Therefore, with each link and each swap the quality of
   the state degrades.  However, it is possible to create higher quality
   Bell Pair states from two or more lower quality Bell Pair states.
   Therefore, once the quality loss over a given distance become
   prohibitive, additional redundancy may be used to restore the state
   quality.

4.4.  Direct transmission vs. swapping

   Direct state transmission whilst simpler conceptually is much more
   demanding to implement reliably in practice which means that any
   near-term practical realisation is more likely to succeed if it is
   based on the Bell Pair and entanglement swapping architecture.  This
   is the architecture that we will focus on in the rest of this memo
   for practical reasons.

   Nevertheless, the direct transmission proposal may be relevant in the
   future as it does enable the fault-tolerant transmission of unknown
   quantum states.  It might even be beneficial to utilise a hybrid
   approach that combines the fault-tolerance of direct transmission



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   with the generic nature of Bell Pairs which lends itself to
   paralellisation and resource provisioning.

5.  Architecture of a quantum internet

5.1.  Model of a quantum network

   A generic quantum network of three nodes could be represented as

   | App |--------------------CC--------------------| App |
      ||                                              ||
    ------                  ------                  ------
   | QNet |-------CC-------| QNet |-------CC-------| QNet |
    ------                  ------                  ------
          \ Bell Pair Gen. / SWAP \ Bell Pair Gen. /
           ----------------        ----------------

   Where "App" is some application running over a quantum network,
   --CC-- denote classical communication links (e.g.  over the public
   Internet or a private LAN), and "QNet" is a generic network stack.
   Architectures for the network stack have been proposed already
   [9][10], but their discussion is beyond the scope of this memo.
   However, they all map onto this generic diagram.  Nodes within a
   quantum network that are capable of performing the entanglement swap
   operation are often referred to as quantum repeaters and we shall
   adopt this terminology from this point on.  End-hosts connecting at
   the edge of the network are not necessarily repeaters themselves.

   The key message here is that a network stack relies on the hardware
   being able to provide two services: Bell Pair generation across a
   link, and swap operation.  In any network model it is assumed that
   the physical device is capable of providing both of these services
   and offers a suitable interface for their usage.

   Strictly speaking (under idealised conditions) quantum memories are
   not needed for a functional quantum network as long as the network is
   able to simultaneously generate all the Bell Pairs, swap the
   entanglement, and deliver the final Bell Pair to the application in a
   usable form.  However, realistically, to be able to provide the two
   services above, the hardware will also need to be able to store the
   qubits in memory which is highly non-trivial.

   Furthermore, it is also assumed that the applications are able to
   communicate classically, and that the nodes themselves are also
   connected over some logical classical channel.  The classical and
   quantum links do not have to coincide.  The classical messaging may
   take a completely different path to the quantum channel as long as




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   the latency characteristics meet the requirements of the control
   protocol.

5.2.  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.  We here
   consider a highly abstract scenario and refer to [5] for pointers to
   the physics literature.

5.2.1.  Fidelity

   The quality of a quantum state is described by a physical quantity
   called fidelity, that takes a value between 0 and 1 (higher is
   better).  Fidelity is the measure of how close a quantum state is to
   the quantum state we desire it to be in.  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 stems from
   the fact that no physical operation is perfect.  Furthermore,
   applications will in general require the fidelity of a quantum state
   to be above some minimum threshold in order to guarantee the
   correctness of their algorithm and it is the responsibility of the
   network to provide such a state.

   Additionally, entanglement swap operations, even if perfect, lead to
   a further reduction in the fidelity of the final state.  Two
   imperfect Bell Pairs when combined will produce a slightly worse Bell
   Pair.  Whilst distillation is one of the available mechanisms to
   correct for these errors it requires additional Bell Pairs to be
   produced.  There will be a trade-off between how much distillation is
   to be done versus what fidelity is acceptable.

   This is a fundamental constraint as perfect noiseless operations and
   lossless communication channels are unachievable.  Therefore, no Bell
   Pair will be generated with perfect fidelity and the network must
   account for this.

5.2.2.  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



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   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.  An architecture that
   handles short lifetimes may also be more cost-efficient in the
   future.

5.2.3.  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
   one in a few thousands will succeed.  Currently, the highest
   achievable rates of success between nodes capable of storing the
   resulting qubits are of the order of 10 Hz.  Combined with short
   memory lifetimes this leads to very tight timing windows to build up
   network-wide connectivity.  Achievable rates are likely to increase
   with time, but just like with quantum memories, it may be more cost-
   efficient in the future to provide low-rate links in some parts of
   the network.

5.2.4.  Communication qubit

   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.

5.2.5.  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.



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5.3.  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 burden on future
   technology.  Redeploying network technology is a non-trivial process.

   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 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.

5.3.1.  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 the classical
   Internet, but it will inevitably evolve with time and the needs of
   its users.  The goals are listed in order of priority which in itself
   may also evolve as the community learns more about the technology.

   1.  Support distributed quantum applications

       The primary purpose of a quantum internet is to run distributed
       quantum algorithms and it is of utmost importance that they can
       run well and efficiently.  Therefore, the needs of quantum
       applications should always be considered first.  The requirements
       for different applications can be found in [5].

       If a network is able to distribute entanglement it is officially
       quantum.  However, if it is unable to distribute these states
       with a sufficiently high fidelity at a reasonable rate for a
       majority of potential applications it is not practical.

   2.  Support tomorrow's distributed quantum applications

       There are many applications already proposed to run over a
       quantum internet.  However, more algorithms will be invented as
       the community grows as well as the robustness and the reliability



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       of the technology.  Any proposed architecture should not
       constrain the capabilities of the network for short-term benefit.

   3.  Hardware heterogeneity

       There are multiple proposals for realising practical quantum
       repeaters and they all have their advantages and disadvantages.
       It is also very likely that the most optimal technologies in the
       future will be hybrid combinations of the many different
       solutions currently under development.  It should be an explicit
       goal of the architecture to allow for a large variety of hardware
       implementations.

   4.  Be flexible with regards to hardware 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.  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.

   5.  Security

       Whilst the priority for the first quantum networks should be to
       simply work, we cannot forget that ultimately they have to also
       be secure.  This has implications for the physical realisations
       (do they satisfy the idealised theoretical models) and also the
       design of the control stack.

       It is actually difficult to guarantee security at the network
       level and even if the network did provide such guarantees, the
       application would still need to perform its own verification
       similarly to how one ensures end-to-end security in classical
       networks.

       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
       authenticity, confidentiality, or integrity of the transmitted
       qubits or the generated entanglement.  Instead, applications such
       as QKD establish such guarantees using the classical network in
       conjunction with he quantum one.  This is much easier than
       demanding that the network deliver secure entanglement, which
       indeed is not needed for quantum applications.




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       Nevertheless, control protocols themselves should be security
       aware in order to protect the operation of the network itself and
       limit disruption.

   6.  Availability and resilience

       A practical and usable network is able to continue to operate
       despite losses and failures, and will be robust to malicious
       actors trying to disable connectivity.  These may be simply
       considered different aspects of security, but it is worthwhile to
       address them explicitly at the architectural level already.

   7.  Easy to manage and monitor

       Quantum networks rely on complex physical phenomena and require
       hardware that is challenging to build.  Furthermore, the quantum
       resources will at first be very scarce and potentially very
       expensive.  This entails a need for a robust management solution.
       It is important that a good management solution needs to come
       with adequate monitoring capabilities.

       Good management solutions may also be key to optimising the
       networks which in turn may be crucial in making them economically
       feasible.  Unlike user data that is transmitted over classical
       networks, quantum networks only need to generate generic Bell
       Pairs.  This leaves a lot of room for pre-allocating resources in
       an efficient manner.

5.3.2.  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
   between success and failure.  For more information about design
   considerations for quantum networks see [9] [10] .

   1.  Bell Pairs are the fundamental building block

       The key service that a quantum network provides is the
       distribution of entanglement between the nodes in a network.
       This point additionally specifies that the entanglement is
       primarily distributed in the form of the entangled Bell Pair
       states which should be used as a building block in providing
       other services, including more complex entangled states.

   2.  Fidelity is part of the service



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       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 should
       essentially be eliminated for most application protocols, many
       quantum applications only need imperfect entanglement to
       function.  However, 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 application's 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.

   3.  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 point is
       crucial in enabling the reuse of resources of a network and 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.

   4.  Time as an expensive resource

       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.

       However, time is only expensive once quantum operations are
       underway.  If no quantum operations are currently being processed
       then the network can use this time to prepare and provision
       resources.

       As hardware improves, the need for carefully timing quantum
       operations may become smaller.  It is currently unknown what the
       cost of these improvements will be, but it is conceivable that
       there is value in having relatively cheap and undemanding links



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       connected at the edges of a network which will have very short
       memory lifetimes and low rates of Bell Pair generation.

   5.  Limit classical communication

       This point offers a practical guideline to the issue of timing.
       A bottleneck in many quantum networked algorithms is the
       classical communication needed between quantum operations to
       synchronise state.  Ideally, classical control mechanisms that
       require increased memory lifetimes should be avoided.

       For example, some quantum protocols may need to perform a
       correction for the random outcome of a quantum measurement.  For
       this, they will block the state from further operations until a
       classical message is received with the information necessary to
       perform the correction.  The time during which the quantum state
       is blocked is effectively wasted.  It reduces the time available
       for subsequent operations possibly rendering the state useless
       for an application.

       Trade-offs that allow a protocol to limit the number of blocking
       classical communication rounds once quantum operations have
       commenced will in general be worth considering.

   6.  Parallelise quantum operations

       A further point to address the issue of timing constraints in the
       network.  The Bell Pairs on the individual links need not be
       generated one after another along the path between the
       communication end-points.  The order does not matter at all.
       Furthermore, the order of the swap operations is flexible as long
       as they don't reduce the fidelity too much.  Parallelising these
       operations is key to optimising quantum protocols.

   7.  Avoid time-based coordination when possible

       A solution to timing constraints is to synchronise clocks and
       agree on the timing of events.  However, such solutions have
       several downsides.  Whilst network clock synchronisation may be
       accurate enough for certain purposes it introduces an additional
       element of complexity, especially when multiple nodes in
       different networks must be synchronised.  Furthermore, clock
       synchronisation will never be perfect and it is conceivable that
       hardware capabilities advance so much that time-based mechanisms
       under-utilise resources in the more efficient parts of the
       network.





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       Nevertheless, it may not be possible to avoid clocks, but such
       solutions should be adequately justified.

   8.  Pre-allocate resources

       Regardless of what application is running over the network it
       will have the same needs as any other application: a number of
       Bell Pairs of sufficient fidelity.  Whilst the fidelity is a
       variable number, the indistinguishability of Bell Pairs means
       that there is lots of flexibility in how a network may provision
       resources to meet demand.  The additional timing constraints mean
       that pre-allocation of resources will be central to a usable
       quantum network.

6.  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.  Even though user data doesn't enter the
   network, it is still possible to attack the control protocols and
   violate the authenticity, confidentiality, and integrity of
   communication.  However, as this is an informational memo it does not
   propose any concrete mechanisms to achieve these goals.

   In summary:

   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 authenticity, confidentiality, or
   integrity of the transmitted qubits or the generated entanglement.
   Instead, applications such as QKD establish such guarantees using the
   classical network in conjunction with he quantum one.  This is much
   easier than demanding that the network deliver secure entanglement.

7.  IANA Considerations

   This memo includes no request to IANA.

8.  Acknowledgements

   The authors of this memo acknowledge funding received the EU Flagship
   on Quantum Technologies, Quantum Internet Alliance.

   The authors would further like to acknowledge Carlo Delle Donne,
   Matthew Skrzypczyk, and Axel Dahlberg for useful discussions on this
   topic prior to the submission of this memo.




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9.  Informative References

   [1]        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>.

   [2]        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>.

   [3]        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>.

   [4]        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>.

   [5]        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>.

   [6]        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>.

   [7]        Muralidharan, S., Kim, J., Lutkenhaus, N., Lukin, M., and
              L. Jiang, "Ultrafast and Fault-Tolerant Quantum
              Communication across Long Distances", Phys. Rev. Lett. 112
              (25-27), 250501, 2014, <https://arxiv.org/abs/1310.5291>.

   [8]        Humphreys, P., Kalb, N., Morits, J., Schouten, R.,
              Vermeulen, R., Twitchen, D., Markham, M., and R. Hanson,
              "Deterministic delivery of remote entanglement on a
              quantum network", Nature 558, 268-273, 2018,
              <https://arxiv.org/abs/1712.07567>.

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




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   [10]       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>.

   [11]       Nielsen, M. and I. Chuang, "Quantum Computation and
              Quantum Information", Cambridge University Press , 2011.

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





















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