]>
Architectural Principles
for a Quantum InternetQuTechBuilding 22Lorentzweg 12628 CJDelftNetherlandsw.kozlowski@tudelft.nlQuTechBuilding 22Lorentzweg 12628 CJDelftNetherlandss.d.c.wehner@tudelft.nlKeio University5322 EndoFujisawaKanagawa252-0882Japanrdv@sfc.wide.ad.jpIndividualbrunorijsman@gmail.comUniversity of Naples Federico IIDepartment of Electrical Engineering and Information TechnologiesClaudio 2180125NaplesItalyangelasara.cacciapuoti@unina.itUniversity of Naples Federico IIDepartment of Electrical Engineering and Information TechnologiesClaudio 2180125NaplesItalymarcello.caleffi@unina.itMercari, Inc.Roppongi Hills Mori Tower 18F6-10-1 Roppongi, Minato-ku106-6118TokyoJapanshota.nagayama@mercari.com
General
Quantum Internet Research GroupQuantum InternetArchitectureRepeaterBell PairEPR PairThe 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 to account for the fundamentally new properties of quantum
entanglement. 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.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
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 , distributed quantum computation , secure quantum computing in the cloud , quantum-enhanced measurement networks , or longer-baseline telescopes . 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 . 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 states exist, there are no robust
protocols for managing such transmissions.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. for an in-depth introduction to
quantum information.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 .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>.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 isa |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 likeINOUT0000010110111110Now, consider performing a CNOT gate on the state with the first
qubit being the control. We apply a two-qubit gate on all the
superposition states:CNOT (|00> + |10>)/sqrt(2) -> (|00> + |11>)/sqrt(2).What is so interesting about this two-qubit gate operation? The final
state is *entangled*. There is no possible way of representing that
quantum state as a product of two individual qubits; they are no longer
independent 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.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.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. This section explains the meaning of quantum connectivity and the
necessary physical processes at an abstract level.A quantum network cannot be built by simply extrapolating all the
classical models to their quantum analogues. Sending qubits over a wire
like we send classical bits is simply not as easy to do. There are
several technological as well as fundamental challenges that make
classical approaches unsuitable in a quantum context.In classical computers and networks we can read out the bits stored
in memory at any time. This is helpful for a variety of purposes such
as copying, error detection and correction, and so on. This is not
possible with qubits.A measurement of a qubit's state will destroy its superposition and
with it any entanglement it may have been part of. Once a qubit is
being processed, it cannot be read out until a suitable point in the
computation, determined by the protocol handling the qubit, has been
reached. Therefore, we cannot use the same methods known from
classical computing for the purposes of error detection and
correction. Nevertheless, quantum error detection and correction
schemes exist that take this problem into account and how a network
chooses to manage errors will have an impact on its architecture.Since directly reading the state of a qubit is not possible, one
could ask 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.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.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.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 () 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 . 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 .Bell pair states are the entangled two-qubit states:
|00> + |11>,
|00> - |11>,
|01> + |10>,
|01> - |10>,
where the constant 1/sqrt(2) normalisation factor has been ignored
for clarity. Any of the four Bell pair states above will do, as it is
possible to transform any Bell pair into another Bell pair with local
operations performed on only one of the qubits. When each qubit in a
Bell pair is held by a separate node, either 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.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.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.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.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 :"At mid-point": in this scheme an entangled photon pair source
sitting midway between the two nodes with matter qubits sends an
entangled photon through a quantum channel to each of the nodes.
There, transducers are invoked to transfer the entanglement from
the flying qubits to the matter qubits. In this scheme, the
transducers know if the transfers succeeded and are able to herald
successful entanglement generation via a message exchange over the
classical channel."At source": in this scheme one of the two nodes sends a flying
qubit that is entangled with one of its matter qubits. A
transducer at the other end of the link will transfer the
entanglement from the flying qubit to one of its matter qubits.
Just like in the previous scheme, the transducer knows if its
transfer succeeded and is able to herald successful entanglement
generation with a classical message sent to the other node."At both end-points": in this scheme both nodes send a flying
qubit that is entangled with one of their matter qubits. A
detector somewhere in between the nodes performs a joint
measurement on the 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.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: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: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
and we will use the same terminology in this memo.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) .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
().Just like classical error correction, quantum error correction
(QEC) encodes logical qubits using several physical (raw) qubits to
protect them from errors described in . 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.Quantum networks have been categorized into three "generations"
based on the error management scheme they employ . 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. summarises the generations.First generationSecond generationThird generationLoss toleranceHeralded entanglement generation (bi-directional classical signaling)Heralded entanglement generation (bi-directional classical signaling)Quantum Error Correction (no classical signaling)Error toleranceEntanglement distillation (bi-directional classical signaling)Entanglement distillation (uni-directional classical signaling) or
Quantum Error Correction (no classical signaling) Quantum Error Correction (no classical signaling)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 ,
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
, 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 ,
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.The three "generations" summarised: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.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.Third generation quantum networks directly transmit QEC
encoded qubits to adjacent nodes, as discussed in . 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.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.It is evident from the previous sections that the fundamental service
provided by a quantum network significantly differs from that of a
classical network. Therefore, it is not surprising that the architecture
of a quantum internet will itself be very different from that of the
classical Internet.This subsection covers the major fundamental challenges building
quantum networks. Here, we only describe the fundamental differences.
Technological limitations are described later.Bell pairs are not equivalent to payload carrying packets.
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."Store and forward" vs "store and swap" quantum networks.
As described in , 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 , will be able
to support a "store and forward" architecture in addition to "store
and swap".An entangled pair is only useful if the locations of both qubits
are known.
A classical network packet logically exists only at one location at
any point in time. If a packet is modified in some way, whether
headers or payload, this information does not need to be conveyed to
anybody else in the network. The packet can be simply forwarded as
before.
In contrast, entanglement is a phenomenon in which two or more
qubits exist in a physically distributed state. Operations on one of
the qubits change the mutual state of the pair. Since the owner of a
particular qubit cannot just read out its state, it must coordinate
all its actions with the owner of the pair's other qubit. Therefore,
the owner of any qubit that is part of an entangled pair must know
the location of its counterpart. Location, in this context, need not
be the explicit spatial location. A relevant pair identifier, a
means of communication between the pair owners, and an association
between the pair ID and the individual qubits is sufficient.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.In this memo we have already covered two different roles that
classical communication must perform:communicate classical bits of information as part of distributed
protocols such as entanglement swapping and teleportation,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 the two planes so that the
control information received on a classical channel can be applied to
the qubits managed by the quantum data plane.Control plane protocols for quantum networks will have
responsibilities similar to their classical counterparts, namely
drawing the network topology, resource management, populating data
plane tables, etc. They will not manipulate quantum data themselves
and they operate by exchanging classical messages only. Therefore
there is no separate quantum and classical control plane. There is
only one network control plane.However, as we have already mentioned earlier in this memo, there
will be two data planes: a classical data plane and a quantum data
plane. The classical data plane processes and forwards classical
packets. The quantum data plane processes and swaps entangled pairs.
Third generation quantum networks may also forward qubits in addition
to swapping Bell pairs.In addition to control plane messages, there will also be control
information messages that operate at the granularity of individual
entangled pairs, such as heralding messages used for elementary link
generation (). In terms of functionality, these
messages are closer to classical packet headers than control plane
messages and thus we consider them to be part of the quantum data
plane. Therefore, a quantum data plane also includes the exchange of
classical control information at the granularity of individual qubits
and entangled pairs.We have identified quantum repeaters as the core building block of
a quantum network. However, a quantum repeater will have to do more
than just entanglement swapping in a functional quantum network. Its
key responsibilities will include:Creating link-local entanglement between neighbouring
nodes.Extending entanglement from link-local pairs to long-range
pairs through entanglement swapping.Performing distillation to manage the fidelity of the produced
pairs.Participating in the management of the network (routing,
etc.).Not all quantum repeaters in the network will be the same; here we
break them down further:Quantum routers (controllable quantum nodes) - A quantum router
is a quantum repeater with a control plane that participates in
the management of the network and will make decisions about which
qubits to swap to generate the requested end-to-end pairs.Automated quantum nodes - An automated quantum node is a data
plane only quantum repeater that does not participate in 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.End-nodes - End-nodes in a quantum network must be able to
receive and handle an entangled pair, but they do not need to be
able to perform an entanglement swap (and thus are not necessarily
quantum repeaters). End-nodes are also not required to have any
quantum memory as certain quantum applications can be realised by
having the end-node measure its qubit as soon as it is
received.Non-quantum nodes - Not all nodes in a quantum network need to
have a quantum data plane. A non-quantum node is any device that
can handle classical network traffic.Additionally, we need to identify two kinds of links that will
be used in a quantum network:Quantum links - A quantum link is a link which can be used to
generate an entangled pair between two directly connected quantum
repeaters. This may include additional mid-point elements
described in . It may also include a
dedicated classical channel that is to be used solely for the
purpose of coordinating the entanglement generation on this
quantum link.Classical links - A classical link is a link between any node
in the network that is capable of carrying classical network
traffic.Note that passive elements, such as optical switches, do not
destroy the quantum state. Therefore, it is possible to connect
multiple quantum nodes with each other over an optical network and
perform optical switching rather than routing via entanglement
swapping at quantum routers. This does require coordination with the
elementary link entanglement generation process and it still requires
repeaters to overcome the short-distance limitations. However, this is
a potentially feasible architecture for local area networks.A two-hop path in a generic quantum network can be represented
as: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 may require negotiation between the end-nodes (possibly
ahead of time), because they must both open a communication end-point
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 Bell pairs do not carry any user data, some of
these operations can be performed before the request is received in
anticipation of the demand.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.Just like classical networks, various boundaries will exist in
quantum networks.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.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.Not only are there physical differences and administrative
boundaries, but there are important distinctions in how errors will be
managed, as described in , 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.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 for pointers to
the physics literature.In addition to discrete operations being imperfect, storing a qubit
in memory is also highly non-trivial. The main difficulty in achieving
persistent storage is that it is extremely challenging to isolate a
quantum system from the environment. The environment introduces an
uncontrollable source of noise into the system which affects the
fidelity of the state. This process is known as decoherence.
Eventually, the state has to be discarded once its fidelity degrades
too much.The memory lifetime depends on the particular physical setup, but
the highest achievable values in quantum network hardware currently
are on the order of seconds although a
lifetime of a minute has also been demonstrated, but these qubits were
not yet connected to a quantum network .
These values have increased tremendously over the lifetime of the
different technologies and are bound to keep increasing. However, if
quantum networks are to be realised in the near future, they need to
be able to handle short memory lifetimes, for example by reducing
latency on critical paths.Entanglement generation on a link between two connected nodes is
not a very efficient process and it requires many attempts to succeed
. 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 lifetimes this leads
to very tight timing windows to build up network-wide
connectivity.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.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.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.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 . 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.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 have to transmit
arbitrary quantum states .
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 and an overview of
use-cases can be found in .Support tomorrow's distributed quantum applications
The only principle of the Internet that should survive indefinitely
is the principle of constant change .
Technical change is continuous and the size and capabilities of the
quantum internet will change by orders of magnitude. Therefore, it
is an explicit goal that a quantum internet architecture be able to
embrace this change. We have the benefit of having been witness to
the evolution of the classical Internet over several decades and
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.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 (). 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.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.
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 .Make them easy to monitor
In order to manage, evaluate the performance of, or debug a network
it is necessary to have the ability to monitor the network while
ensuring there will be mechanisms in place to protect the
confidentiality and integrity of the devices connected to it.
Quantum networks bring new challenges in this area so it should be a
goal of a quantum network architecture to make this task easy.
The fundamental unit of quantum information, the qubit, cannot be
actively monitored as any readout irreversibly destroys its
contents. One of the implications of this fact is that measuring an
individual pair's fidelity is impossible. Fidelity is meaningful
only as a statistical quantity 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
metadata. It is impossible to extract this information from the
qubits themselves. This implies that tracking entangled pairs
necessitates some exchange of classical information. This
information might include (i) a reference to the entangled pair that
allows distributed applications to coordinate actions on qubits of
the same pair, (ii) the two bits from each entanglement swap
necessary to identify the final state of the Bell pair ().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.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 .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) as this may be more
efficient under certain circumstances.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.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.Time is part of the service
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).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.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 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).
However, note that the definition of "shortest-path"/"least-cost" may be
different in a quantum network to account for its non-classical features,
such as fidelity .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.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).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.This memo includes no request to IANA.The authors want to thank Carlo Delle Donne, Matthew Skrzypczyk, Axel
Dahlberg, Mathias van den Bossche, Patrick Gelard, Chonggang Wang, Scott
Fluhrer, Joey Salazar, Joseph Touch, and the rest of the QIRG community as
a whole for their very useful reviews and comments to the document.
&rfc1958;
&I-D.irtf-qirg-quantum-internet-use-cases;
Quantum cryptography: Public key distribution and coin tossingQuantum cryptography based on Bell's theoremSecure multi-party quantum computationQuantum-enhanced measurements: beating the standard quantum
limitThe Quantum Internet has arrived (and it hasn't)Quantum internet: A vision for the road aheadExperimental tests of realistic local theories via Bell's theoremOptimal architectures for long distance quantum communicationDesigning quantum repeater networksAttacking the quantum internetThe network impact of hijacking a quantum repeaterA link layer protocol for quantum networksDancing with QubitsQuantum Computation and Quantum InformationMixed state entanglement and quantum error correctionQuantum repeaters: The role of imperfect local operations in
quantum communicationWhen Entanglement meets Classical Communications: Quantum
Teleportation for the Quantum InternetDistributing graph states over arbitrary quantum networksPath selection for quantum repeater networksThe design philosophy of the DARPA internet protocolsQuantum NetworkingThe engineering of software-defined quantum key distribution networksThe SECOQC quantum key distribution network in ViennaLoophole-free {Bell} inequality violation using electron spins separated by 1.3 kilometresUnconditionally verifiable blind quantum computationIs entanglement monogamous?The concept of transition in quantum mechanicsA single quantum cannot be clonedSurface code quantum communicationLonger-baseline telescopes using quantum repeatersThe Quantum Protocol ZooEntanglement purification and quantum error correctionThe Quantum InternetQuantum error correction for beginnersQuantum repeaters based on atomic ensembles and linear opticsOne-second coherence for a single electron spin coupled to a multi-qubit nuclear-spin environmentA 10-qubit solid-state spin register with quantum memory up to one minute