Quantum Internet Research Group W. Kozlowski
Internet-Draft S. Wehner
Intended status: Informational QuTech
Expires: May 6, 2020 R. Van Meter
Keio Univeristy
B. Rijsman
Individual
November 3, 2019
Architectural Principles for a Quantum Internet
draft-irtf-qirg-principles-02
Abstract
The vision of a quantum internet is to fundamentally enhance Internet
technology by enabling quantum communication between any two points
on Earth. To achieve this goal, a quantum network stack should be
built from the ground up as the physical nature of the communication
is fundamentally different. The first realisations of quantum
networks are imminent, but there is no practical proposal for how to
organise, utilise, and manage such networks. In this memo, we
attempt lay down the framework and introduce some basic architectural
principles for a quantum internet. This is intended for general
guidance and general interest, but also to provide a foundation for
discussion between physicists and network specialists.
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
Internet-Drafts are working documents of the Internet Engineering
Task Force (IETF). Note that other groups may also distribute
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and may be updated, replaced, or obsoleted by other documents at any
time. It is inappropriate to use Internet-Drafts as reference
material or to cite them other than as "work in progress."
This Internet-Draft will expire on May 6, 2020.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Model of communication . . . . . . . . . . . . . . . . . . . 3
2.1. Qubit . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2. Multiple qubits . . . . . . . . . . . . . . . . . . . . . 4
3. Entanglement as the fundamental service . . . . . . . . . . . 6
4. Achieving quantum connectivity . . . . . . . . . . . . . . . 7
4.1. Challenges . . . . . . . . . . . . . . . . . . . . . . . 7
4.1.1. The measurement problem . . . . . . . . . . . . . . . 8
4.1.2. No-cloning theorem . . . . . . . . . . . . . . . . . 8
4.1.3. Fidelity . . . . . . . . . . . . . . . . . . . . . . 8
4.2. Bell pairs . . . . . . . . . . . . . . . . . . . . . . . 9
4.3. Teleportation . . . . . . . . . . . . . . . . . . . . . . 10
4.4. The life cycle of entanglement . . . . . . . . . . . . . 10
4.4.1. Link generation . . . . . . . . . . . . . . . . . . . 10
4.4.2. Entanglement swapping . . . . . . . . . . . . . . . . 11
4.4.3. Direct transmission vs. entanglement swapping . . . . 13
5. Architecture of a quantum internet . . . . . . . . . . . . . 13
5.1. New challenges . . . . . . . . . . . . . . . . . . . . . 13
5.2. Classical communication . . . . . . . . . . . . . . . . . 15
5.3. Abstract model of the network . . . . . . . . . . . . . . 15
5.3.1. Elements of a quantum network . . . . . . . . . . . . 15
5.3.2. Putting it all together . . . . . . . . . . . . . . . 16
5.4. Network boundaries . . . . . . . . . . . . . . . . . . . 17
5.4.1. Boundaries between different physical architectures . 17
5.4.2. Boundaries between different administrative regions . 18
5.5. Physical constraints . . . . . . . . . . . . . . . . . . 18
5.5.1. Memory lifetimes . . . . . . . . . . . . . . . . . . 18
5.5.2. Rates . . . . . . . . . . . . . . . . . . . . . . . . 18
5.5.3. Communication qubit . . . . . . . . . . . . . . . . . 19
5.5.4. Homogeneity . . . . . . . . . . . . . . . . . . . . . 19
5.6. Architectural principles . . . . . . . . . . . . . . . . 19
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5.6.1. Goals of a quantum internet . . . . . . . . . . . . . 20
5.6.2. The principles of a quantum internet . . . . . . . . 22
6. Security Considerations . . . . . . . . . . . . . . . . . . . 24
7. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 25
8. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 25
9. Informative References . . . . . . . . . . . . . . . . . . . 25
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 26
1. Introduction
Quantum networks are distributed systems of quantum devices that
utilise fundamental quantum mechanical phenomena such as
superposition, entanglement, and quantum measurement to achieve
capabilities beyond what is possible with classical networks.
Depending on the stage of a quantum network [5] such devices may be
simple photonic devices capable of preparing and measuring only one
quantum bit (qubit) at a time, all the way to large-scale quantum
computers of the future. A quantum network is not meant to replace
classical networks, but rather form an overall hybrid classical
quantum network supporting new capabilities which are otherwise
impossible to realise. This new networking paradigm offers promise
for a range of new applications such as secure communications [1],
distributed quantum computation [2], or quantum sensor networks [3].
The field of quantum communication has been a subject of active
research for many years and the most well-known application of
quantum communication, quantum key distribution (QKD) for secure
communications, has already been deployed at short (roughly 100km)
distances.
Fully quantum networks capable of transmitting and managing entangled
quantum states in order to send, receive, and manipulate distributed
quantum information are now imminent [4] [5]. Whilst a lot of effort
has gone into physically realising and connecting such devices, and
making improvements to their speed and error tolerance there are no
worked out proposals for how to run these networks. To draw an
analogy with a classical network, we are at a stage where we can
start to physically connect our devices and send data, but all
sending, receiving, buffer management, connection synchronisation,
and so on, must be managed by the application itself at what is even
lower than assembly level where no common interfaces yet exist.
Furthermore, whilst physical mechanisms for forwarding quantum states
exist, there are no robust protocols for managing such transmissions.
2. Model of communication
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
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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. [10] for an in-depth introduction to
quantum information.
2.1. Qubit
The differences between quantum computation and classical computation
begin at the bit-level. A classical computer operates on the binary
alphabet { 0, 1 }. A quantum bit, a qubit, exists over the same
binary space, but unlike the classical bit, it can exist in a so-
called superposition of the two possibilities:
a |0> + b |1>,
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 [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>
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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
+----+-----+
| 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
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before, but the states of the two qubits following a measurement will
always be identical.
Once a measurement is performed, the two qubits are once again
independent. The final state is either |00> or |11> and both of
these states can be trivially decomposed into a product of two
individual qubits. The entanglement has been consumed and if the
same measurement is to be repeated, the entangled state must be
prepared again.
3. Entanglement as the fundamental service
Entanglement is the fundamental building block of quantum networks.
To see this, consider the state from the previous section:
(|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
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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.
It is impossible to entangle two qubits without ever having them
directly interact with each other (e.g. by performing a local two-
qubit gate, such as the CNOT). A local - or mediated - interaction
is necessary to create entanglement and thus such states cannot be
created between two quantum nodes that cannot transmit quantum states
to each other. Therefore, it is the transmission of qubits that
draws the line between a genuine quantum network and a collection of
quantum computers connected over a classical network.
A quantum network is defined as a collection of nodes that is able to
exchange qubits and distribute entangled states amongst themselves.
A quantum 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. [5]>
4. Achieving quantum connectivity
This section explains the meaning of quantum connectivity and the
necessary physical processes at an abstract level.
4.1. Challenges
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.
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4.1.1. The measurement problem
In classical computers and networks we can read out the bits stored
in memory at any time. This is helpful for a variety of purposes
such as copying, error detection and correction, and so on. This is
not possible with qubits.
A measurement of a qubit's state will destroy its superposition and
with it any entanglement it may have been part of. Once a qubit is
being processed, it cannot be read out until a suitable point in the
computation, determined by the protocol handling the qubit, has been
reached. Therefore, we cannot use the same methods known from
classical computing for the purposes of error detection and
correction.
4.1.2. No-cloning theorem
Since directly reading the state of a qubit is not possible, one
could ask the question if we can simply copy a qubit without looking
at it. Unfortunately, this is fundamentally not possible in quantum
mechanics.
The no-cloning theorem states that it is impossible to create an
identical copy of an arbitrary unknown quantum state. Therefore, it
is also impossible to use the same mechanisms that worked for
classical networks for signal amplification, retransmission, and so
on as they all rely on the ability to copy the underlying data.
Since any physical channel will always be lossy, connecting nodes
within a quantum network is a challenging endeavour and its
architecture must at its core address this very issue.
4.1.3. Fidelity
In general, it is expected that a classical packet arrives at its
destination without any errors introduced by hardware noise along the
way. This is verified at various levels through a variety of
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).
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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.
4.2. Bell pairs
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 [7]. 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 state above will do as it is
possible to transform any Bell pair into another Bell pair with local
operations performed on only one of the qubits. That is, either of
the nodes that hold the two qubits of the Bell pair can apply a
series of single qubit gates to just their qubit in order to
transform the ensemble between the different variants.
Distributing a Bell pair between two nodes is much easier than
transmitting an arbitrary quantum state over a network. Since the
state is known handling errors becomes easier and small-scale error-
correction (such as entanglement distillation 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
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set of basis states. Maximal entanglement means that these states
have the strongest non-classical correlations of all possible two-
qubit states. Furthermore, since single-qubit local operations can
never increase entanglement, less entangled states would impose some
constraints on distributed quantum algorithms. This makes Bell pairs
particularly useful as a generic building block for distributed
quantum applications.
4.3. Teleportation
The observation that we only need to be able to distribute Bell pairs
relies on the fact that this enables the distribution of any other
arbitrary entangled state. This can be achieved via quantum state
teleportation. Quantum state teleportation consumes an unknown
quantum state that we want to transmit and recreates it at the
desired destination. This does not violate the no-cloning theorem as
the original state is destroyed in the process.
To achieve this, an entangled pair needs to be distributed between
the source and destination before teleportation commences. The
source then entangles the transmission qubit with its end of the pair
and performs a read out 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 never entered the
network itself. Therefore, the network needs to only be able to
reliably produce Bell pairs between any two nodes in the network.
4.4. The life cycle of entanglement
Reducing the problem of quantum connectivity to one of generating a
Bell pair has facilitated the problem, but it has not solved it. In
this section we discuss, how these entangled pairs are generated in
the first place, and how its two qubits are delivered to the end-
points.
4.4.1. Link generation
[waiting for contrib]
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4.4.2. Entanglement swapping
The problem with generating entangled pairs directly across a link is
that its efficiency decreases with its length. Beyond a few 10s of
kms 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:
+---------+ +---------+ +---------+
| A | | B | | C |
| |------| |------| |
| X1~~~~~~~~~~X2 Y1~~~~~~~~~~Y2 |
+---------+ +---------+ +---------+
where X1 and X2 are the qubits of the entangled pair X and Y1 and Y2
are the qubits of entangled pair Y. The entanglement is denoted with
~~. In the diagram above nodes A and B share the pair X and nodes B
and C share the pair Y, but we want entanglement between A and C.
To achieve this goal we simply teleport the qubit X2 using the pair
Y. This requires node B to 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:
+---------+ +---------+ +---------+
| A | | B | | C |
| |------| |------| |
| X1~~~~~~~~~~~~~~~~~~~~~~~~~~~X2 |
+---------+ +---------+ +---------+
Depending on the needs of the network and/or application a final
Pauli correction at the recipient node may not be necessary since the
result of this operation is also a Bell pair. However, the two
classical bits that form the read out from the measurement at node B
must still be communicated, because they carry information about
which of the four Bell pairs was actually produced. If a correction
is not performed, the recipient must be informed which Bell pair was
received.
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This process of teleporting Bell pairs using other entangled pairs is
called entanglement swapping.
4.4.2.1. Distillation
Neither the generation of Bell pairs nor the swapping operations are
noiseless operations. Therefore, with each link and each swap the
fidelity of the state degrades. However, it is possible to create
higher fidelity Bell pair states from two or more lower fidelity
pairs through a process called distillation or purification.
To purify 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.
Purification makes low demands on fidelity and resources, but
distributed protocols incur round-trip delays [11].
4.4.2.2. Delivery
The bare minimum requirements of an application for every Bell pair
delivered to the two end-nodes are:
1. Information about which of the four Bell pairs was delivered.
The network may choose to not perform Pauli corrections at all
and simply notify the application of which state the delivered
pair is in or it may perform the Pauli corrections and always
deliver the same state.
2. An identifier that allows the applicatqion to unambiguously
determine which qubits at the two end-points belong to which
entangled pair.
3. An estimate of the fidelity of the delivered pair. This should
be above the minimum threshold determined by the application.
However, this will only be an estimate and not a guarantee. This
has security implications for applications which will be
discussed in the section on security.
There are several other features an application might want to be able
to request (e.g. multiple pairs delivered together close in time, but
doesn't matter when they are delivered), but they are beyond the
scope of this memo.
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4.4.3. Direct transmission vs. entanglement 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. All
near-term experimental implementations of quantum repeaters are based
on this approach. Therefore, this is the architecture that we will
focus on in the rest of this memo.
Nevertheless, the direct transmission proposal may be relevant in the
future as it has better fault-tolerance properties and much better
scaling with transmission distance. It might even be beneficial to
utilise a hybrid approach that combines the fault-tolerance of direct
transmission with the generic nature of Bell pairs which lends itself
to paralellisation and resource provisioning. That is, we still use
Bell pairs for transmission of user data, but direct transmission may
be used for some of hops for the purposes of Bell pair generation
rather than just relying solely on entanglement swapping.
5. Architecture of a quantum internet
It is evident from the previous sections that the fundamental service
provided by a quantum network significantly differs from that of a
classical network. Therefore, it is not surprising that the
architecture of a quantum internet will itself be very different from
that of the classical Internet.
5.1. New challenges
This subsection covers the major fundamental challenges building
quantum networks. Here, we only describe the fundamental
differences, technological limitations are described later.
1. There is no quantum equivalent of a payload carrying packet.
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
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information via separate classical channels which the repeaters
will have to correlate with the qubits stored in their memory.
2. 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.
3. 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 repeater 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.
4. Generating end-to-end entanglement is a parallelisable operation.
Classical packets carry user data from source destination by
performing a series of hops across the network. This process is
necessarily sequential -- it is impossible to forward a packet
ahead of time as the user data it carries cannot be known in
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advance. A quantum network does not carry any user data. It is
only responsible for generating entangled pairs in any of the
generic Bell states. The process of creating an end-to-end Bell
pair is by its nature parallelisable -- all of the individual
link pairs can be generated independently of one another.
Furthermore, there is no ordering requirement on the entanglement
swapping operations either, they can happen in any order as long
as the network can keep track of which pairs were swapped so that
it can correctly identify the two ends of the final Bell pair.
This parallelism must be exploited to make the most efficient use
of the quantum network's resources.
5.2. Classical communication
In this memo we have already covered two different roles that
classical communication must perform:
o communicate classical bits of information as part of distributed
protocols such as entanglement swapping and teleportation,
o communicate control information within a network - 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.
5.3. Abstract model of the network
5.3.1. Elements of a quantum network
Collecting all the pieces described so far, a quantum network will
consist of the following elements:
o Quantum repeaters - A quantum repeater is a node in the network
that is capable of generating entangled pairs with its directly
connected neighbours and performing entanglement swap operations
on them.
o Quantum routers - A quantum router is a quantum repeater that is
connected to more than two quantum repeaters as neighbours. This
distinguishes it from quantum repeaters composed into a linear
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chain to connect two quantum routers (since no-cloning prohibits
quantum signal amplification).
o End-nodes - End-nodes in a quantum network must be able to receive
and handle an entangled pair, but they do not need to be able to
perform an entanglement swap (and thus are not necessarily quantum
repeaters). End-nodes are also not required to have any quantum
memory as certain quantum applications can be realised by having
the end-node measure its qubit as soon as it is received.
o Non-quantum nodes - Not all nodes in a quantum network need to
have a quantum data plane. A non-quantum node is any device that
can handle classical network traffic.
o Quantum links - A quantum link is a link which can be used to
generate an entangled pair between two directly connected quantum
repeaters. It may include a dedicated classical channel that is
to be used solely for the purpose of coordinating the entanglement
generation on this quantum link.
o Classical links - A classical link is a link between any node in
the network that is capable of carrying classical network traffic.
5.3.2. Putting it all together
A two-hop path in a generic quantum network can be represented as:
| App |-------------------CC-------------------| App |
|| ||
------ ------ ------
| EN |----QC & CC----| QR |----QC & CC----| EN |
------ ------ ------
App - user-level application
QR - quantum repeater
EN - end-node
QC - quantum channel
CC - classical channel
An application running on two end-nodes attached to a network will at
some point need the network to generate entangled pairs for its use.
This will require negotiation between the end-nodes, because they
must both open a communication end-point (a quantum socket) which the
network can use to identify the two ends of the connection. The two
end-nodes use the classical connectivity available in the network to
achieve this goal.
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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.
5.4. Network boundaries
Just like classical network, there will various boundaries will exist
in quantum networks.
5.4.1. Boundaries between different physical architectures
There are many different physical architectures for implementing
quantum repeater technology. The different technologies differ in
how they store and manipulate qubits in memory and how they generate
entanglement across a link with their neighbours. Different
architectures come with different trade-offs and thus a functional
network will likely consist of a mixture of different types of
quantum repeaters.
For example, architectures based on optical elements and atomic
ensembles are very efficient at generating entanglement, but provide
little control over the qubits once the pair is generated. On the
other hand nitrogen-vacancy architectures offer a much greater degree
of control over qubits, but have a harder time generating the
entanglement across a link.
It is an open research question where exactly the boundary will lie.
It could be that a single quantum repeater node provides some
backplane connection between the architectures, but it also could be
that special quantum links delineate the boundary.
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5.4.2. Boundaries between different administrative regions
Just like in classical networks, multiple quantum networks will
connect into a global quantum internet. This necessarily implies the
existence of borders between different administrative regions. How
these boundaries will be handled is also an open question and thus
beyond the scope of this memo.
5.5. Physical constraints
The model above has effectively abstracted away the particulars of
the hardware implementation. However, certain physical constraints
need to be considered in order to build a practical network. Some of
these are fundamental constraints and no matter how much the
technology improves, they will always need to be addressed. Others
are artefacts of the early stages of a new technology. We here
consider a highly abstract scenario and refer to [5] for pointers to
the physics literature.
5.5.1. Memory lifetimes
In addition to discrete operations being imperfect, storing a qubit
in memory is also highly non-trivial. The main difficulty in
achieving persistent storage is that it is extremely challenging to
isolate a quantum system from the environment. The environment
introduces an uncontrollable source of noise into the system which
affects the fidelity of the state. This process is known as
decoherence. Eventually, the state has to be discarded once its
fidelity degrades too much.
The memory lifetime depends on the particular physical setup, but the
highest achievable values currently are on the order of seconds.
These values have increased tremendously over the lifetime of the
different technologies and are bound to keep increasing. However, if
quantum networks are to be realised in the near future, they need to
be able to handle short memory lifetimes. An architecture that
handles short lifetimes may also be more cost-efficient in the
future.
5.5.2. Rates
Entanglement generation on a link between two connected nodes is not
a very efficient process and it requires many attempts to succeed. A
fast repetition rate for Bell Pair generation is achievable, but only
one in a few thousands will succeed. Currently, the highest
achievable rates of success between nodes capable of storing the
resulting qubits are of the order of 10 Hz. Combined with short
memory lifetimes this leads to very tight timing windows to build up
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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.
5.5.3. Communication qubit
Most physical architectures capable of storing qubits are only able
to generate entanglement using only a subset of its available qubits
called communication qubits. Once a Bell Pair has been generated
using a communication qubit, its state can be transferred into
memory. This may impose additional limitations on the network. In
particular if a given node has only one communication qubit it cannot
simultaneously generate Bell Pairs over two links. It must generate
entanglement over the links one at a time.
5.5.4. Homogeneity
Currently all hardware implementations are homogeneous and they do
not interface with each other. In general, it is very challenging to
combine different quantum information processing technologies at
present. Coupling different technologies with each other is of great
interest as it may help overcome the weaknesses of the different
implementations, but this may take a long time to be realised with
high reliability and thus is not a near-term goal.
5.6. Architectural principles
Given that the most practical way of realising quantum network
connectivity is using Bell Pair and entanglement swapping repeater
technology what sort of principles should guide us in assembling such
networks such that they are functional, robust, efficient, and most
importantly: they work. Furthermore, how do we design networks so
that they work under the constraints imposed by the hardware
available today, but do not impose unnecessary burden on future
technology. Redeploying network technology is a non-trivial process.
As this is a completely new technology that is likely to see many
iterations over its lifetime, this memo must not serve as a
definitive set of rules, but merely as a general set of recommended
guidelines based on principles and observations made by the
community. The benefit of having a community built document at this
early stage is that expertise in both quantum information and network
architecture is needed in order to successfully build a quantum
internet.
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5.6.1. Goals of a quantum internet
When outlining any set of principles we must ask ourselves what goals
do we want to achieve as inevitably trade-offs must be made. So what
sort of goals should drive a quantum network architecture? The
following list has been inspired by the history of 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 protocols and it is of utmost importance that they can
run well and efficiently. Therefore, the needs of quantum
applications should always be considered first. The requirements
for different applications can be found in [5].
If a network is able to distribute entanglement it is officially
quantum. However, if it is unable to distribute these states
with a sufficiently high fidelity at a reasonable rate for a
majority of potential applications it is not practical.
2. Support tomorrow's distributed quantum applications
There are many applications already proposed to run over a
quantum internet. However, more algorithms will be invented as
the community grows as well as the robustness and the reliability
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
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capabilities of repeaters will improve and redeploying a
technology is extremely challenging.
5. Security
Whilst the priority for the first quantum networks should be to
simply work, we cannot forget that ultimately they have to also
be secure. This has implications for the physical realisations
(do they satisfy the idealised theoretical models) and also the
design of the control stack.
It is actually difficult to guarantee security at the network
level and even if the network did provide such guarantees, the
application would still need to perform its own verification
similarly to how one ensures end-to-end security in classical
networks.
It turns out that as long as the underlying implementation
corresponds to (or sufficiently approximates) theoretical models
of quantum cryptography, quantum cryptographic protocols do not
need the network to provide any guarantees about the
authenticity, confidentiality, or integrity of the transmitted
qubits or the generated entanglement. Instead, applications such
as QKD establish such guarantees using the classical network in
conjunction with he quantum one. This is much easier than
demanding that the network deliver secure entanglement, which
indeed is not needed for quantum applications.
Nevertheless, control protocols themselves should be security
aware in order to protect the operation of the network itself and
limit disruption.
6. Availability and resilience
A practical and usable network is able to continue to operate
despite losses and failures, and will be robust to malicious
actors trying to disable connectivity. These may be simply
considered different aspects of security, but it is worthwhile to
address them explicitly at the architectural level already.
7. Easy to manage and monitor
Quantum networks rely on complex physical phenomena and require
hardware that is challenging to build. Furthermore, the quantum
resources will at first be very scarce and potentially very
expensive. This entails a need for a robust management solution.
It is important that a good management solution needs to come
with adequate monitoring capabilities.
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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.
5.6.2. The principles of a quantum internet
The principles support the goals, but are not goals themselves. The
goals define what we want to build and the principles provide a
guideline in how we might achieve this. The goals will also be the
foundation for defining any metric of success for a network
architecture, whereas the principles in themselves do not distinguish
between success and failure. For more information about design
considerations for quantum networks see [8] [9] .
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
In addition to being able to deliver Bell Pairs to the
communication end-points, the Bell Pairs must be of sufficient
fidelity. Unlike in classical networks where errors should
essentially be eliminated for most application protocols, many
quantum applications only need imperfect entanglement to
function. However, different applications will have different
requirements for what fidelity they can work with. It is the
network's responsibility to balance the resource usage with
respect to the application's requirements. It may be that it is
cheaper for the network to provide lower fidelity pairs that are
just above the threshold required by the application than it is
to guarantee high fidelity pairs to all applications regardless
of their requirements.
3. Bell Pairs are indistinguishable
Any two Bell Pairs between the same two nodes are
indistinguishable for the purposes of an application provided
they both satisfy its required fidelity threshold. This point is
crucial in enabling the reuse of resources of a network and for
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the purposes of provisioning resources to meet application
demand. However, the qubits that make up the pair themselves are
not indistinguishable and the two nodes operating on a pair must
coordinate to make sure they are operating on qubits that belong
to the same Bell Pair.
4. Time as an expensive resource
With the current technology, time is the most expensive resource.
It is not the only resource that is in short supply (memory, and
communication qubits are as well), but ultimately it is the
lifetime of quantum memories that imposes the most difficult
conditions for operating an extended network of quantum nodes.
Current hardware has low rates of Bell Pair generation, short
memory lifetimes, and access to a limited number of communication
qubits. All these factors combined mean that even a short
waiting queue at some node could be enough for the Bell Pairs to
decohere.
However, time is only expensive once quantum operations are
underway. If no quantum operations are currently being processed
then the network can use this time to prepare and provision
resources.
As hardware improves, the need for carefully timing quantum
operations may become smaller. It is currently unknown what the
cost of these improvements will be, but it is conceivable that
there is value in having relatively cheap and undemanding links
connected at the edges of a network which will have very short
memory lifetimes and low rates of Bell Pair generation.
5. Limit classical communication
This point offers a practical guideline to the issue of timing.
A bottleneck in many quantum networked algorithms is the
classical communication needed between quantum operations to
synchronise state. Ideally, classical control mechanisms that
require increased memory lifetimes should be avoided.
For example, some quantum protocols may need to perform a
correction for the random outcome of a quantum measurement. For
this, they will block the state from further operations until a
classical message is received with the information necessary to
perform the correction. The time during which the quantum state
is blocked is effectively wasted. It reduces the time available
for subsequent operations possibly rendering the state useless
for an application.
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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
Bell Pairs of sufficient fidelity. Whilst the fidelity is a
variable number, the indistinguishability of Bell Pairs means
that there is lots of flexibility in how a network may provision
resources to meet demand. The additional timing constraints mean
that pre-allocation of resources will be central to a usable
quantum network.
6. Security Considerations
Even though no user data enters a quantum network security is listed
as an explicit goal for the architecture and this issue is addressed
in the section on goals. Even though user data doesn't enter the
network, it is still possible to attack the control protocols and
violate the authenticity, confidentiality, and integrity of
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communication. However, as this is an informational memo it does not
propose any concrete mechanisms to achieve these goals.
In summary:
As long as the underlying implementation corresponds to (or
sufficiently approximates) theoretical models of quantum
cryptography, quantum cryptographic protocols do not need the network
to provide any guarantees about the authenticity, confidentiality, or
integrity of the transmitted qubits or the generated entanglement.
Instead, applications such as QKD establish such guarantees using the
classical network in conjunction with he quantum one. This is much
easier than demanding that the network deliver secure entanglement.
7. IANA Considerations
This memo includes no request to IANA.
8. Acknowledgements
The authors of this memo acknowledge funding received 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.
9. Informative References
[1] Bennett, C. and G. Brassard, "Quantum cryptography: Public
key distribution and coin tossing", Theoretical Computer
Science 560, 7-11, 2014,
.
[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,
.
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[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] Meter, R. and J. Touch, "Designing quantum repeater
networks", IEEE Communications Magazine 51, 64-71, 2013,
.
[9] Dahlberg, A., Skrzypczyk, M., Coopmans, T., Wubben, L.,
Rozpedek, F., Pompili, M., Stolk, A., Pawelczak, P.,
Knegjens, R., de Oliveira Filho, J., Hanson, R., and S.
Wehner, "A Link Layer Protocol for Quantum Networks",
arXiv 1903.09778, 2019,
.
[10] Nielsen, M. and I. Chuang, "Quantum Computation and
Quantum Information", Cambridge University Press , 2011.
[11] Bennett, C., DiVincenzo, D., Smolin, J., and W. Wootters,
"Mixed State Entanglement and Quantum Error Correction",
Phys. Rev. A Vol. 54, Iss. 5, 1996,
.
Authors' Addresses
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Wojciech Kozlowski
QuTech
Building 22
Lorentzweg 1
Delft 2628 CJ
Netherlands
Email: w.kozlowski@tudelft.nl
Stephanie Wehner
QuTech
Building 22
Lorentzweg 1
Delft 2628 CJ
Netherlands
Email: S.D.C.Wehner@tudelft.nl
Rodney Van Meter
Keio Univeristy
5322 Endo
Fujisawa, Kanagawa 252-0882
Japan
Email: rdv@sfc.wide.ad.jp
Bruno Rijsman
Individual
Email: brunorijsman@gmail.com
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