Quantum Internet Research Group W. Kozlowski
Internet-Draft QuTech
Intended status: Informational March 9, 2019
Expires: September 10, 2019
Architectural Principles for a Quantum Internet
draft-irtf-qirg-principles-00
Abstract
The vision of a quantum internet is to fundamentally enhance Internet
technology by enabling quantum communication between any two points
on Earth. To achieve this goal, a quantum network stack must be
built from the ground up as the physical nature of the communication
is fundamentally different. The first realisations of quantum
networks are imminent, but there is no practical proposal for how to
organise, utilise, and manage such networks. In this memo, we
attempt lay down the framework and introduce some basic architectural
principles for a quantum internet. This is intended for general
guidance and general interest, but also to provide a foundation for
discussion between physicists and network specialists.
Status of This Memo
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This Internet-Draft will expire on September 10, 2019.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Model of computation . . . . . . . . . . . . . . . . . . . . 3
2.1. Qubit . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2. Multiple qubits . . . . . . . . . . . . . . . . . . . . . 4
3. Entanglement as the fundamental service . . . . . . . . . . . 5
4. Achieving quantum connectivity . . . . . . . . . . . . . . . 7
4.1. No-cloning theorem . . . . . . . . . . . . . . . . . . . 7
4.2. Direct transmission . . . . . . . . . . . . . . . . . . . 7
4.3. Bell pairs and entanglement swapping . . . . . . . . . . 7
4.3.1. Bell Pairs . . . . . . . . . . . . . . . . . . . . . 7
4.3.2. Teleportation . . . . . . . . . . . . . . . . . . . . 8
4.3.3. Bell Pair links and entanglement swapping . . . . . . 9
4.3.4. Distillation . . . . . . . . . . . . . . . . . . . . 9
4.4. Direct transmission vs. swapping . . . . . . . . . . . . 10
5. Architecture of a quantum internet . . . . . . . . . . . . . 10
5.1. Model of a quantum network . . . . . . . . . . . . . . . 10
5.2. Physical constraints . . . . . . . . . . . . . . . . . . 11
5.2.1. Fidelity . . . . . . . . . . . . . . . . . . . . . . 11
5.2.2. Memory lifetimes . . . . . . . . . . . . . . . . . . 12
5.2.3. Rates . . . . . . . . . . . . . . . . . . . . . . . . 12
5.2.4. Communication qubit . . . . . . . . . . . . . . . . . 12
5.2.5. Homogeneity . . . . . . . . . . . . . . . . . . . . . 13
5.3. Architectural principles . . . . . . . . . . . . . . . . 13
5.3.1. Goals of a quantum internet . . . . . . . . . . . . . 13
5.3.2. The principles of a quantum internet . . . . . . . . 15
6. Security Considerations . . . . . . . . . . . . . . . . . . . 18
7. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 18
8. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 18
9. Informative References . . . . . . . . . . . . . . . . . . . 18
Author's Address . . . . . . . . . . . . . . . . . . . . . . . . 19
1. Introduction
Quantum networks are distributed systems of quantum computers that
utilise fundamental quantum mechanical phenomena such as
superposition, entanglement, and quantum measurement to achieve
capabilities beyond what is possible with classical networks. This
new networking paradigm offers promise for a range of new
applications such as tamper-proof communications [1], distributed
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quantum computation [2], and quantum sensor networks [3]. The field
of quantum communication has been a subject of active research for
many years and the most well-known application of quantum computers
that has already been deployed, quantum key distribution (QKD), is a
protocol used for secure communications.
Fully quantum networks capable of transmitting and managing entangled
states in order to send, receive, and manipulate distributed quantum
states are now imminent [4] [5]. Whilst a lot of effort has gone
into physically connecting the devices and bringing down the error
rates there are no concrete proposals for how to run these networks.
To draw an analogy with a classical network, we are at a stage where
we can 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 essentially
assembly level. Furthermore, whilst physical mechanisms for
forwarding quantum states exist, there are no protocols for managing
it.
2. Model of computation
In order to understand the framework for quantum networking a basic
understanding of quantum information is necessary. The following
sections aim to introduce the bare minimum necessary to be understand
the principles of operation of a quantum network. This exposition
was written with a classical networking audience in mind. It is
assumed that the reader has never before been exposed to any quantum
physics.
2.1. Qubit
The differences between quantum computation and classical computation
begin at the bit-level. A classical computer operates on the binary
alphabet { 0, 1 }. A quantum bit, a qubit, exists over the same
binary space, but unlike the classical bit, it can exist in a so-
called superposition of the two possibilities:
a |0> + b |1>,
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. The
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probability of measuring the state in the |0> state is |a|^2 and
similarly the probability of measuring the state in the |1> state
is |b|^2. This randomness is not due to our ignorance of the
underlying mechanisms, but rather it is a fundamental feature of a
quantum mechanical system [6].
The superposition property plays an important role in fundamental
gate operations on qubits. Since a qubit can exist in a
superposition of its basis states, the elementary quantum gates are
able to act on all states of the superposition at the same time. For
example, consider the NOT gate:
NOT (a |0> + b |1>) -> a |1> + b |0>.
2.2. Multiple qubits
When multiple qubits are combined in a single quantum state the space
of possible states grows exponentially and all these states can
coexist in a superposition. For example, the general form of a two
qubit register is
a |00> + b |01> + c |10> + d |11>
where the coefficients have the same probability amplitude
interpretation as for the single qubit state. Each state represents
a possible outcome of a measurement of the two qubit register. For
example, |01>, denotes a state in which the first qubit is in the
state |0> and the second is in the state |1>.
Performing single qubit gates affects the relevant qubit in each of
the superposition states. Similarly, two qubit gates also act on all
the relevant superposition states, but their outcome is far more
interesting.
Consider a two qubit register where the first qubit is in the
superposed state (|0> + |1>)/sqrt(2) and the other is in the
state |0>. This combined state can be written as:
(|0> + |1>)/sqrt(2) x |0> = (|00> + |10>)/sqrt(2),
where x denotes a tensor product (the mathematical mechanism for
combining quantum states together). Let us now consider the two-
qubit CNOT gate. The CNOT gate takes as input two qubits, a control
and target, and applies the NOT gate to the target if the control
qubit is set. The truth table looks like
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+----+-----+
| IN | OUT |
+----+-----+
| 00 | 00 |
| 01 | 01 |
| 10 | 11 |
| 11 | 10 |
+----+-----+
Now, consider performing a CNOT gate on the ensemble with the first
qubit being the control. We apply a two qubit gate on all the
superposition states:
CNOT (|00> + |10>)/sqrt(2) -> (|00> + |11>)/sqrt(2).
What is so interesting about this two-qubit gate operation? The
final state is *entangled*. There is no possible way of representing
that quantum state as a product of two individual qubits, they are no
longer independent and their behaviour cannot be fully described
without accounting for the other qubit. The states of the two
individual qubits are now correlated beyond what is possible to
achieve classically. Neither qubit is in a definite |0> or |1>
state, but if we perform a measurement on either one, the outcome of
the partner qubit will *always* yield the exact same outcome. The
final state, whether it's |00> or |11>, is fundamentally random as
before, but the states of the two qubits following a measurement will
always be identical.
Once a measurement is performed, the two qubits are once again
independent. The final state is either |00> or |11> and both of
these states can be trivially decomposed into a product of two
individual qubits. The entanglement has been consumed and if the
same measurement is to be repeated, the entangled state must be
prepared again.
3. Entanglement as the fundamental service
Entanglement is the fundamental building block of quantum networks.
To see this, consider the final 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.
Now consider sending one of the qubits to another device. This
device can be anywhere: on the other side of the room, in a different
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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 these non-classical correlations in order to design
completely new types of algorithms that are not possible to achieve
with just classical communication. Examples of such applications are
quantum cryptography, blind quantum computation, or distributed
quantum computation.
As a trivial example consider the problem of reaching consensus
between two nodes. The two nodes want to agree on the value of a
single bit. In a quantum network they can simply request the network
to generate the state (|00> + |11>)/sqrt(2) for them and that is
essentially all that needs to be done. 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, 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.
However, it is impossible to entangle two qubits without ever having
them directly interact with each other (e.g. by performing a local
two-qubit gate, such as the CNOT). A local interaction is necessary
to create entanglement and thus such states cannot be created between
two quantum computers that cannot transmit quantum states to each
other. Therefore, it is the entanglement property of multi-qubit
states 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
distribute entangled states amongst themselves. A quantum computer
that is able to communicate classically with another quantum computer
is not a member of a quantum network.
This is a crucial difference between classical and quantum networks.
Classical applications transmit data over the network to synchronise
distributed state. Quantum network applications obtain distributed
states, synchronised at the physical level via entanglement, from the
network to perform quantum algorithms.
More complex services and applications can be built on top of
entangled states distributed by the network.
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4. Achieving quantum connectivity
4.1. No-cloning theorem
To build a network we must first physically connect all the nodes
with quantum channels that enable them to distribute the
entanglement. Unfortunately, our ability to transfer quantum states
is complicated by the no-cloning theorem.
The no-cloning theorem states that it is impossible to create an
identical copy of an arbitrary unknown quantum state. Since
performing a measurement on a quantum state destroys its
superposition, there is no practical way of learning the exact state
of a qubit in an unknown state. Therefore, it is impossible to use
the same mechanisms that worked for classical networks for error-
correction, amplification, retransmission, and so on as they all rely
on the ability to copy the underlying data. Since any physical
channel will always be lossy, connecting a quantum network is a
challenging endeavour and its architecture must at its core address
this very issue.
4.2. Direct transmission
The most straightforward way to distribute an entangled state is to
simply transmit one of the qubits directly to the other end across a
series of nodes while performing sufficient error correction to bring
losses down to an acceptable level. Despite the no-cloning theorem
and the inability to directly measure a quantum state error-
correcting mechanisms for quantum communication exist [7]. However,
even in the most optimistic scenarios the hardware requirements to
fault-tolerantly transmit a single qubit are beyond near-term
capabilities. Nevertheless, due to the promise of fault-tolerance
and its favourable poly-logarithmic scaling with distance, this may
eventually become a desirable method for entanglement distribution.
4.3. Bell pairs and entanglement swapping
4.3.1. Bell Pairs
An alternative relies on the observation that we do not need to be
able to distribute any arbitrary entangled quantum state. We only
need to be able to distribute any one of what are known as the Bell
Pair states. Bell Pair states are the entangled two-qubit states:
|00> + |11>,
|00> - |11>,
|01> + |10>,
|01> - |10>,
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where the constant 1/sqrt(2) normalisation factor has been ignored
for clarity. Any of the four Bell Pair state above will do as it is
possible to transform any Bell Pair into another Bell Pair with local
operations performed on only one of the qubits. That is, either of
the nodes that hold the two qubits of the Bell Pair can apply a
series of single qubit gates to just their qubit in order to
transform the ensemble between the different variants.
Distributing a Bell Pair between two nodes is much easier than
transmitting an arbitrary quantum state over a network. Since the
state is known error-correction is easier and error-detection
combined with reattempts becomes a valid strategy.
The reason for using Bell Pairs specifically as opposed to any other
two-qubit state, is that they are the maximally entangled two-qubit
set of basis states. Maximal entanglement means that these states
have the strongest non-classical correlations of all possible two-
qubit states. Furthermore, since single-qubit local operations can
never increase entanglement, less entangled states would impose some
constraints on distributed quantum algorithms. This makes Bell Pairs
particularly useful as a generic building block for distributed
quantum applications.
4.3.2. Teleportation
The observation that we only need to be able to distribute Bell Pairs
relies on the fact that this enables the distribution of any other
arbitrary entangled state. This can be achieved via quantum state
teleportation. Quantum state teleportation consumes an unknown
quantum state that we want to transmit and recreates it at the
desired destination.
To achieve this, a Bell Pair needs to be distributed between the
source and destination. The source then entangles the transmission
qubit with its end of the Bell Pair and performs a measurement. This
consumes the Bell Pair's entanglement turning the source and
destination qubits into independent states. However, this process
transforms the Bell Pair's qubit at the destination into the
transmission qubit's original state. Note he process requires the
source to also communicate its two-bit measurement result so that the
destination can correct for the randomness of the outcome.
The unknown quantum state that was transmitted never entered the
network itself. Therefore, the network needs to only be able to
reliably produce Bell Pairs between any two nodes in the network.
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4.3.3. Bell Pair links and entanglement swapping
Reducing the problem to one of generating a Bell Pair state has
facilitated the problem, but it has not solved it.
The technology to generate a Bell Pair between two directly connected
quantum nodes already exists and has been demonstrated in laboratory
conditions [8]. Interestingly, neither of the two qubits of the pair
need to be transmitted any further.
A Bell Pair between any two nodes in the network can be constructed
from Bell Pairs generated along each individual link on the path
between the two end-points. Each node along the path can consume the
two Bell Pairs on the two links that it is connected to in order to
produce a new Bell Pair between the two far ends. This process is
known as entanglement swapping. Pictorially it can be represented as
follows:
x~~~~~~~~~~~~~x x~~~~~~~~~~~~~x
[ ]-----------[ ]-----------[ ]
where x~~x denotes a Bell Pair with individual qubits represented by
x, -- denotes a quantum link, and [ ] denotes a node. The diagram
above represents the situation after the middle node has generated a
Bell Pair with two of its directly connected neighbours. Now, the
middle node performs an entanglement swap operation (the exact
details of the mechanism are beyond the scope of this memo). This
operation consumes the two Bell Pairs and produces a new Bell Pair
between the two far ends of this three-node network as follows:
x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x
[ ]-----------[ ]-----------[ ]
The outcome is guaranteed to be a Bell Pair between the two end
nodes, but which of the four possible Bell Pairs is produced is not
deterministic. However, the middle node will know which one was
produced as the entanglement swap is a measurement operation that
yields two classical bits. The final state can be inferred from this
two-bit readout. Therefore, the middle node needs only to
communicate the outcome over a classical channel to one or both ends
who can apply a correction to transform the pair into any of its
other forms (if so desired).
4.3.4. Distillation
Neither the Bell Pair or the swapping operations are lossless
operations. Therefore, with each link and each swap the quality of
the state degrades. However, it is possible to create higher quality
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Bell Pair states from two or more lower quality Bell Pair states.
Therefore, once the quality loss over a given distance become
prohibitive, additional redundancy may be used to restore the state
quality.
4.4. Direct transmission vs. swapping
Direct state transmission whilst simpler conceptually is much more
demanding to implement reliably in practice which means that any
near-term practical realisation is more likely to succeed if it is
based on the Bell Pair and entanglement swapping architecture. This
is the architecture that we will focus on in the rest of this memo
for practical reasons.
Nevertheless, we are not entirely discarding the direct transmission
proposal. Whilst it does enable the fault-tolerant transmission of
unknown quantum states, it might still be more beneficial to use it
to distribute Bell Pairs instead. Distributing Bell Pairs via direct
transmission means that one can leverage the advantages of
entanglement swapping which allows for paralellisation as the Bell
Pairs can be built up from both ends simultaneously. Furthermore,
the generic nature of the Bell Pair means that a network may
provision resources better before it receives any request.
5. Architecture of a quantum internet
5.1. Model of a quantum network
A generic quantum network of three nodes could be represented as
| App |--------------------CC--------------------| App |
|| ||
------ ------ ------
| QNet |-------CC-------| QNet |-------CC-------| QNet |
------ ------ ------
\ Bell Pair Gen. / SWAP \ Bell Pair Gen. /
---------------- ----------------
Where "App" is some application running over a quantum network,
--CC-- denote classical communication links (e.g. over the public
Internet or a private LAN), and "QNet" is a generic network stack.
Architectures for the network stack have been proposed already [9],
but their discussion is beyond the scope of this memo. However, they
all map onto this generic diagram. Nodes within a quantum network
that are capable of performing the entanglement swap operation are
often referred to as quantum repeaters and we shall adopt this
terminology from this point on. End-hosts connecting at the edge of
the network are not necessarily repeaters themselves.
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The key message here is that a network stack relies on the hardware
being able to provide two services: Bell Pair generation across a
link, and swap operation. In any network model it is assumed that
the physical device is capable of providing both of these services
and offers a suitable interface for their usage.
Strictly speaking quantum memories are not needed for a functional
quantum network as long as the network is able to generate the Bell
Pairs, swap the entanglement, and deliver the final Bell Pair to the
application in a usable form. However, in general, to be able to
provide the two services above, the hardware will also need to be
able to store the qubits in memory which is highly non-trivial.
Furthermore, it is also assumed that the applications are able to
communicate classically, and that the nodes themselves are also
connected over some classical channel. The classical links between
the nodes need not always have an associated quantum link, but it is
assumed that any quantum link has a classical link running in
parallel.
5.2. Physical constraints
The model above has effectively abstracted away the particulars of
the hardware implementation. However, certain physical constraints
need to be considered in order to build a practical network. Some of
these are fundamental constraints and no matter how much the
technology improves, they will always need to be addressed. Others
are artefacts of the early stages of a new technology.
5.2.1. Fidelity
The quality of a quantum state is described by a physical quantity
called fidelity. Fidelity is the measure of how close a quantum
state is to the quantum state we desire it to be in. It expresses
the probability that one state will pass a test to identify as the
other.
Fidelity is an important property of a quantum system that stems from
the fact that no physical operation is perfect. Furthermore,
applications will in general require the fidelity of a quantum state
to be above some minimum threshold in order to guarantee the
correctness of their algorithm and it is the responsibility of the
network to provide such a state.
Additionally, entanglement swap operations, even if perfect, lead to
a further reduction in the fidelity of the final state. Two
imperfect Bell Pairs when combined will produce a slightly worse Bell
Pair. Whilst distillation is one of the available mechanisms to
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correct for these errors it requires additional Bell Pairs to be
produced. There will be a trade-off between how much distillation is
to be done versus what fidelity is acceptable.
This is a fundamental constraint as perfect noiseless operations and
lossless communication channels are unachievable. Therefore, no Bell
Pair will be generated with perfect fidelity and the network must
account for this.
5.2.2. Memory lifetimes
In addition to discrete operations being imperfect, storing a qubit
in memory is also highly non-trivial. The main difficulty in
achieving persistent storage is that it's 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 hundreds of
milliseconds. These values have increased tremendously over the
lifetime of the different technologies and are bound to keep
increasing. However, if quantum networks are to be realised in the
near future, they need to be able to handle short memory lifetimes.
An architecture that handles short lifetimes may also be more cost-
efficient in the future.
5.2.3. Rates
Entanglement generation on a link between two connected nodes is not
a very efficient process and it requires many attempts to succeed. A
fast repetition rate for Bell Pair generation is achievable, but only
one in a few thousands will succeed. Currently, the highest
achievable rates of success are of the order of 10 Hz. Combined with
short memory lifetimes this leads to very tight timing windows to
build up network-wide connectivity. Achievable rates are likely to
increase with time, but just like with quantum memories, it may be
more cost-efficient in the future to provide low-rate links in some
parts of the network.
5.2.4. Communication qubit
Some physical architectures are not able to generate entanglement
using any memory qubit that they have access to. In these systems,
entanglement is generated using a communication qubit and once a Bell
Pair has been generated, the qubit state is transferred into memory.
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This may impose additional limitations on the network. In particular
if a given node has only one communication qubit it cannot
simultaneously generate Bell Pairs over two links. It must generate
entanglement over the links one at a time.
5.2.5. Homogeneity
Currently all hardware implementations are homogeneous and they do
not interface with each other. In general, it is very challenging to
combine different quantum information processing technologies due to
their sensitivity to losses. Coupling different technologies with
each other is of great interest as it may help overcome the
weaknesses of the different implementations, but this is not a near-
term goal.
5.3. Architectural principles
Given that the most practical way of realising quantum network
connectivity is using Bell Pair and entanglement swapping repeater
technology what sort of principles should guide us in assembling such
networks such that they are functional, robust, efficient, and most
importantly: they work. Furthermore, how do we design networks so
that they work under the constraints imposed by the hardware
available today, but do not impose unnecessary burden on future
technology. Redeploying network technology is a non-trivial process.
As this is a completely new technology that is likely to see many
iterations over its lifetime, this memo must not serve as a
definitive set of rules, but merely as a general guide based on
principles and observations made by the community. The benefit of
having a community built document at this early stage is that
expertise in both quantum information and network architecture is
needed in order to successfully build a quantum internet.
5.3.1. Goals of a quantum internet
When outlining any set of principles we must ask ourselves what goals
do we want to achieve as inevitably trade-offs must be made. So what
sort of goals should drive a quantum network architecture? The
following list has been inspired by the history of the classical
Internet, but it will inevitably evolve with time and the needs of
its users. The goals are listed in order of priority which in itself
may also evolve as the community learns more about the technology.
1. Support distributed quantum applications
The primary purpose of a quantum internet is to run distributed
quantum algorithms and it is of utmost importance that they can
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run well and efficiently. Therefore, the needs of quantum
applications should always be considered first.
If a network is able to distribute entanglement it is officially
quantum. However, if it is unable to distribute these states
with a sufficiently high fidelity at a reasonable rate for a
majority of potential applications it is not practical.
2. Support tomorrow's distributed quantum applications
There are many applications already proposed to run over a
quantum internet. However, more algorithms will be invented as
the community grows as well as the robustness and the reliability
of the technology. Any proposed architecture should not
constrain the capabilities of the network for short-term benefit.
3. Hardware heterogeneity
There are multiple proposals for realising practical quantum
repeaters and they all have their advantages and disadvantages.
It is also very likely that the most optimal technologies in the
future will be hybrid combinations of the many different
solutions currently under development. It should be an explicit
goal of the architecture to allow for a large variety of hardware
implementations.
4. Be flexible with regards to hardware capabilities and limitations
This goal encompasses two important points. First, the
architecture should be able to function under the physical
constraints imposed by the current generation hardware. Second,
it should not make it difficult to run the network over any
hardware that may come along in the future. The physical
capabilities of repeaters will improve and redeploying a
technology is extremely challenging.
5. Security, availability, and resilience
Whilst the priority for the first quantum networks should be to
simply work, we cannot forget that ultimately they have to also
be secure. There are three key security considerations at the
network level, confidentiality, integrity, and authenticity.
Confidentiality and integrity - it is vital that the network can
provide a reasonable guarantee of the minimum fidelity of a
delivered Bell Pair as the application's own security mechanisms
rely on this. Uncertainty about the fidelity of a Bell Pair may
potentially expose its data to an eavesdropper.
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Authenticity - it is important that any application can have
confidence that the other end of the Bell Pair has been delivered
to the desired partner.
Additionally 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.
6. Easy to manage and monitor
Quantum networks rely on complex physical phenomena and require
hardware that is challenging to build. Furthermore, the quantum
resources will at first be very scarce and potentially very
expensive. This entails a need for a robust management solution.
It is important that a good management solution needs to come
with adequate monitoring capabilities.
Good management solutions may also be key to optimising the
networks which in turn may be crucial in making them economically
feasible. Unlike user data that is transmitted over classical
networks, quantum networks only need to generate generic Bell
Pairs. This leaves a lot of room for pre-allocating resources in
an efficient manner.
5.3.2. The principles of a quantum internet
The principles support the goals, but are not goals themselves. The
goals define what we want to build and the principles provide a
guideline in how we might achieve this. The goals will also be the
foundation for defining any metric of success for a network
architecture, whereas the principles in themselves do not distinguish
between success and failure.
1. Bell Pairs are the fundamental building block
The key service that a quantum network provides is the
distribution of entanglement between the nodes in a network.
This point additionally specifies that the entanglement is
primarily distributed in the form of the entangled Bell Pair
states which should be used as a building block in providing
other services, including more complex entangled states.
2. Fidelity is part of the service
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In addition to being able to deliver Bell Pairs to the
communication end-points, the Bell Pairs must be of sufficient
fidelity. However, different applications will have different
requirements for what fidelity they can work with. It is the
network's responsibility to balance the resource usage with
respect to the application's requirements. It may be that it is
cheaper for the network to provide lower fidelity pairs that are
just above the threshold required by the application than it is
to guarantee high fidelity pairs to all applications regardless
of their requirements.
3. Bell Pairs are indistinguishable
Any two Bell Pairs between the same two nodes are
indistinguishable for the purposes of an application provided
they both satisfy its required fidelity threshold. This point is
crucial in enabling the reuse of resources of a network and for
the purposes of provisioning resources to meet application
demand.
4. Time as an expensive resource
With the current technology, time is the most expensive resource.
It is not the only resource that is in short supply (memory, and
communication qubits are as well), but ultimately it is the
lifetime of quantum memories that imposes the most difficult
conditions for operating an extended network of quantum nodes.
Current hardware has low rates of Bell Pair generation, short
memory lifetimes, and access to a limited number of communication
qubits. All these factors combined mean that even a short
waiting queue at some node could be enough for the Bell Pairs to
decohere.
However, time is only expensive once quantum operations are
underway. If no quantum operations are currently being processed
then the network can use this time to prepare and provision
resources.
As hardware improves, the need for carefully timing quantum
operations may become smaller. It is currently unknown what the
cost of these improvements will be, but it is conceivable that
there is value in having relatively cheap and undemanding links
connected at the edges of a network which will have very short
memory lifetimes and low rates of Bell Pair generation.
5. Limit classical communication
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This point offers a practical guideline to the issue of timing.
A bottleneck in many quantum networked algorithms is the
classical communication needed between quantum operations to
synchronise state.
For example, some quantum protocols may need to perform a correct
for the random outcome of a quantum measurement. For this, they
will block the state from further operations until a classical
message is received with the information necessary to perform the
correction. The time during which the quantum state is blocked
is effectively wasted. It reduces the time available for
subsequent operations possibly rendering the state useless for an
application.
Trade-offs that allow a protocol to limit the number of blocking
classical communication rounds once quantum operations have
commenced will in general be worth considering.
6. Parallelise quantum operations
A further point to address the issue of timing constraints in the
network. The Bell Pairs on the individual links need not be
generated one after another along the path between the
communication end-points. The order does not matter at all.
Furthermore, the order of the swap operations is flexible as long
as they don't reduce the fidelity too much. Parallelising these
operations is key to optimising quantum protocols.
7. Avoid time-based coordination when possible
A solution to timing constraints is to synchronise clocks and
agree on the timing of events. However, such solutions have
several downsides. Whilst network clock synchronisation may be
accurate enough for certain purposes it introduces an additional
element of complexity, especially when multiple nodes in
different networks must be synchronised. Furthermore, clock
synchronisation will never be perfect and it is conceivable that
hardware capabilities advance so much that time-based mechanisms
under-utilise resources in the more efficient parts of the
network.
Nevertheless, it may not be possible to avoid clocks, but such
solutions should be adequately justified.
8. Pre-allocate resources
Regardless of what application is running over the network it
will have the same needs as any other application: a number of
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Bell Pairs of sufficient fidelity. Whilst the fidelity is a
variable number, the indistinguishability of Bell Pairs means
that there is lots of flexibility in how a network may provision
resources to meet demand. The additional timing constraints mean
that pre-allocation of resources will be central to a usable
quantum network.
6. Security Considerations
Even though no user data enters a quantum network security is
explicitly listed as a goal in this memo. However, as this is an
informational memo it does not propose any concrete mechanisms to
achieve these goals.
In summary:
o Confidentiality and integrity in the quantum context is the
network's guarantee on the minimum fidelity of the delivered Bell
Pair states. Uncertainty about the fidelity of a Bell Pair may
potentially expose an application to an eavesdropper.
o Authenticity in a quantum network is the guarantee that the other
end of the Bell Pair is with the requested partner and not any
other third party.
7. IANA Considerations
This memo includes no request to IANA.
8. Acknowledgements
The author would like to acknowledge funding received the Quantum
Internet Alliance.
The author would further like to acknowledge Stephanie Wehner, Carlo
Delle Donne, Matthew Skrzypczyk, and Axel Dahlberg for useful
discussions on this topic prior to the submission of this memo.
9. Informative References
[1] Bennett, C. and G. Brassard, "Quantum cryptography: Public
key distribution and coin tossing", Theoretical Computer
Science 560, 7-11, 2014,
.
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[2] Crepeau, C., Gottesman, D., and A. Smith, "Secure multi-
party quantum computation. Proceedings of Symposium on
Theory of Computing", Proceedings of Symposium on Theory
of Computing , 2002,
.
[3] Giovanetti, V., Lloyd, S., and L. Maccone, "Quantum-
enhanced measurements: beating the standard quantum
limit", Science 306(5700), 1330-1336, 2004,
.
[4] Castelvecchi, D., "The Quantum Internet has arrived (and
it hasn't)", Nature 554, 289-292, 2018,
.
[5] Wehner, S., Elkouss, D., and R. Hanson, "Quantum internet:
A vision for the road ahead", Science 362, 6412, 2018,
.
[6] Aspect, A., Grangier, P., and G. Roger, "Experimental
Tests of Realistic Local Theories via Bell's Theorem",
Phys. Rev. Lett. 47 (7): 460-463, 1981,
.
[7] Muralidharan, S., Kim, J., Lutkenhaus, N., Lukin, M., and
L. Jiang, "Ultrafast and Fault-Tolerant Quantum
Communication across Long Distances", Phys. Rev. Lett. 112
(25-27), 250501, 2014, .
[8] Humphreys, P., Kalb, N., Morits, J., Schouten, R.,
Vermeulen, R., Twitchen, D., Markham, M., and R. Hanson,
"Deterministic delivery of remote entanglement on a
quantum network", Nature 558, 268-273, 2018,
.
[9] Meter, R. and J. Touch, "Designing quantum repeater
networks", IEEE Communications Magazine 51, 64-71, 2013,
.
Author's Address
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Wojciech Kozlowski
QuTech
Building 22
Lorentzweg 1
Delft 2628 CJ
Netherlands
Phone: +31 (0)15 2787077
Email: w.kozlowski@tudelft.nl
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