]>
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.it
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 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.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 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 , or quantum sensor networks . 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 what is even lower
than assembly level 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 so-called
superposition of the two possibilities:a |0> + b |1>,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, 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
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 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.Entanglement is the fundamental building block of quantum networks. To
see this, 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 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.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. One cannot just send qubits
like one can send bits over a wire. 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.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
checksums. Since we cannot read or copy a quantum state a similar
approach is out of question for quantum networks.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 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 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 it 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.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. 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 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 on 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.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 its 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, the so-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" scheme: the key idea is that an entangled pair
source sends an entangled photon through a quantum channel to each
of the nodes, where 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" scheme: the key idea is that 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. Also in this 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" scheme: the key idea is that 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. In this
scheme, 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" scheme is more robust to photon loss, but in the
other schemes the nodes retain greater control over the entangled pair
generation.The problem with generating entangled pairs directly across a link
is that its efficiency decreases with its 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 the 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 performs 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 transmitted and 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 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, but
distributed protocols incur round-trip delays .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 pairs are handled individually -- they are
not grouped into packets and they 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.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, 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 - this includes
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, it must be
able to correlate information between them so that the control
information received on a classical channel can be applied to the qubits
managed by the quantum data plane.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
pairsParticipate 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. It may include a dedicated classical channel that is to
be used solely for the purpose of coordinating the entanglement
generation on this quantum link.Classical links - A classical link is a link between any node
in the network that is capable of carrying classical network
traffic.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 will require negotiation between the end-nodes, because they must
both open a communication end-point (a quantum socket) which the
network can use to identify the two ends of the connection. The two
end-nodes use the classical connectivity available in the network to
achieve this goal.When the network receives a request to generate end-to-end entangled
pairs it uses the classical communication channels to coordinate and
claim the resources necessary to fulfil 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 control information is distributed the network
performs the necessary quantum operations such as generating entangled
over individual links, performing entanglement swaps, and further
signalling to transmit the swap outcomes and other control
information. Since none of the entangled pairs carry any 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 once 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.Just like classical network, there will 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.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 currently are on the order of seconds.
These values have increased tremendously over the lifetime of the
different technologies and are bound to keep increasing. However, if
quantum networks are to be realised in the near future, they need to
be able to handle short memory lifetimes, for example by reducing
latency on critical paths.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 of 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 burden 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 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.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 certainly not the most basic one possible. For
example, QKD, the most well known quantum application protocol only
relies on the stronger than classical correlations and inherent
secrecy of entangled Bell pairs and does not transmit arbitrary
quantum states.
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 .Support tomorrow's distributed quantum applications
Early-stage quantum networks will be very limited in terms of their
capabilities and will only be able to run a limited set of
applications. As quantum repeater technology becomes more advanced
and acquire more sophisticated capabilities, new applications will
become possible. The different stages of this development are
described in .
Therefore, it is important that any proposed architecture for
general purpose quantum repeater networks should not constrain their
potential capabilities for the benefit of being able to run
early-stage applications more efficiently. 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 more sophisticated applications.Support hardware 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.
Whilst conceptually they are all capable of the same tasks 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 support from the
beginning.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.Ensure security at the network level
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 is particularly important for quantum networks given
that one of the key driving factors for the technology is the
enhance security offered by quantum entanglement. 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 in the first place.
Nevertheless, control protocols themselves should be security aware
in order to protect the operation of the network itself and limit
disruption. This will primarily involve securing the classical
control and management traffic by means of authentication and
possibly encryption.Make them easy to manage and monitor
The fundamental unit of quantum information, the qubit, cannot be
actively monitored as any readout irreversibly destroys its
contents. Furthermore, given one end of an entangled pair, it is
impossible to tell where the other qubit is without any additional
information. Therefore, monitoring quantum networks will be more
challenging and more important if any meaningful network management
solution is to be developed.Ensure 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. The coexistence of
two separate channels, a quantum and a classical one, will likely
prove to be challenging.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 .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.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.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 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.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.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
(ISIS).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 ISIS 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 as 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).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.This memo includes no request to IANA.The authors of this memo acknowledge funding received from the EU
Flagship on Quantum Technologies through Quantum Internet Alliance
project.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.Quantum cryptography: Public key distribution and coin
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Teleportation for the Quantum Internet