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draft-irtf-qirg-principles-06.txt
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draft-irtf-qirg-principles-06.txt
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Quantum Internet Research Group W. Kozlowski
Internet-Draft S. Wehner
Intended status: Informational QuTech
Expires: 2 October 2021 R. Van Meter
Keio University
B. Rijsman
Individual
A. S. Cacciapuoti
M. Caleffi
University of Naples Federico II
S. Nagayama
Mercari, Inc.
31 March 2021
Architectural Principles for a Quantum Internet
draft-irtf-qirg-principles-06
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 to account for the fundamentally new
properties of quantum entanglement. The first realisations of
quantum entanglement networks are imminent, but there is no practical
proposal for how to organise, utilise, and manage such networks. In
this memo, we attempt to lay down the framework and introduce some
basic architectural principles for a quantum internet. This is
intended for general guidance and general interest, but also to
provide a foundation for discussion between physicists and network
specialists.
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
working documents as Internet-Drafts. The list of current Internet-
Drafts is at https://datatracker.ietf.org/drafts/current/.
Internet-Drafts are draft documents valid for a maximum of six months
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."
Kozlowski, et al. Expires 2 October 2021 [Page 1]
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This Internet-Draft will expire on 2 October 2021.
Copyright Notice
Copyright (c) 2021 IETF Trust and the persons identified as the
document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents (https://trustee.ietf.org/
license-info) in effect on the date of publication of this document.
Please review these documents carefully, as they describe your rights
and restrictions with respect to this document. Code Components
extracted from this document must include Simplified BSD License text
as described in Section 4.e of the Trust Legal Provisions and are
provided without warranty as described in the Simplified BSD License.
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Quantum information . . . . . . . . . . . . . . . . . . . . . 4
2.1. Qubit . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2. Multiple qubits . . . . . . . . . . . . . . . . . . . . . 5
3. Entanglement as the fundamental resource . . . . . . . . . . 6
4. Achieving quantum connectivity . . . . . . . . . . . . . . . 8
4.1. Challenges . . . . . . . . . . . . . . . . . . . . . . . 8
4.1.1. The measurement problem . . . . . . . . . . . . . . . 8
4.1.2. No-cloning theorem . . . . . . . . . . . . . . . . . 9
4.1.3. Fidelity . . . . . . . . . . . . . . . . . . . . . . 9
4.1.4. Inadequacy of direct transmission . . . . . . . . . . 10
4.2. Bell pairs . . . . . . . . . . . . . . . . . . . . . . . 10
4.3. Teleportation . . . . . . . . . . . . . . . . . . . . . . 11
4.4. The life cycle of entanglement . . . . . . . . . . . . . 12
4.4.1. Elementary link generation . . . . . . . . . . . . . 12
4.4.2. Entanglement swapping . . . . . . . . . . . . . . . . 13
4.4.3. Error Management . . . . . . . . . . . . . . . . . . 14
4.4.4. Delivery . . . . . . . . . . . . . . . . . . . . . . 17
5. Architecture of a quantum internet . . . . . . . . . . . . . 17
5.1. Challenges . . . . . . . . . . . . . . . . . . . . . . . 18
5.2. Classical communication . . . . . . . . . . . . . . . . . 19
5.3. Abstract model of the network . . . . . . . . . . . . . . 20
5.3.1. The control and data planes . . . . . . . . . . . . . 20
5.3.2. Elements of a quantum network . . . . . . . . . . . . 21
5.3.3. Putting it all together . . . . . . . . . . . . . . . 22
5.4. Network boundaries . . . . . . . . . . . . . . . . . . . 23
5.4.1. Boundaries between different physical
architectures . . . . . . . . . . . . . . . . . . . . 23
5.4.2. Boundaries between different administrative
regions . . . . . . . . . . . . . . . . . . . . . . . 24
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5.4.3. Boundaries between different error management
schemes . . . . . . . . . . . . . . . . . . . . . . . 24
5.5. Physical constraints . . . . . . . . . . . . . . . . . . 24
5.5.1. Memory lifetimes . . . . . . . . . . . . . . . . . . 24
5.5.2. Rates . . . . . . . . . . . . . . . . . . . . . . . . 25
5.5.3. Communication qubits . . . . . . . . . . . . . . . . 25
5.5.4. Homogeneity . . . . . . . . . . . . . . . . . . . . . 25
6. Architectural principles . . . . . . . . . . . . . . . . . . 25
6.1. Goals of a quantum internet . . . . . . . . . . . . . . . 26
6.2. The principles of a quantum internet . . . . . . . . . . 29
7. A thought experiment inspired by classical networks . . . . . 31
8. Security Considerations . . . . . . . . . . . . . . . . . . . 33
9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 33
10. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 33
11. Informative References . . . . . . . . . . . . . . . . . . . 33
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 39
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 non-quantum (classical)
networks [Kimble08]. Depending on the stage of a quantum network
[Wehner18] such devices may range from 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
[VanMeterBook].
This new networking paradigm offers promise for a range of new
applications such as quantum cryptography [Bennett14] [Ekert91],
distributed quantum computation [Crepeau02], secure quantum computing
in the cloud [Fitzsimons17], quantum-enhanced measurement networks
[Giovanetti04], or higher-precision, long-baseline telescopes
[Gottesman12]. 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 [Elliott03] [Peev09] [Aguado19].
Fully quantum networks capable of transmitting and managing entangled
quantum states in order to send, receive, and manipulate distributed
quantum information are now imminent [Castelvecchi18] [Wehner18].
Whilst a lot of effort has gone into physically realising and
connecting such devices [Hensen15], and making improvements to their
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speed and error tolerance, there are no worked out proposals for how
to run these networks. To draw an analogy with a classical network,
we are at a stage where we can start to physically connect our
devices and send data, but all sending, receiving, buffer management,
connection synchronisation, and so on, must be managed by the
application itself at a level below conventional assembly language,
where no common interfaces yet exist. Furthermore, whilst physical
mechanisms for transmitting quantum states exist, there are no robust
protocols for managing such transmissions.
2. Quantum information
In order to understand the framework for quantum networking, a basic
understanding of quantum information is necessary. The following
sections aim to introduce the bare minimum necessary to understand
the principles of operation of a quantum network. This exposition
was written with a classical networking audience in mind. It is
assumed that the reader has never before been exposed to any quantum
physics. We refer to e.g. [SutorBook] [NielsenChuang] 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, called a qubit, exists over the
same binary space, but unlike the classical bit, it can exist in a
superposition of the two possibilities:
a |0> + b |1>,
where |X> is Dirac's ket notation for a quantum state, here the
binary 0 and 1, and the coefficients a and b are complex numbers
called probability amplitudes. Physically, such a state can be
realised using a variety of different technologies such as electron
spin, photon polarisation, atomic energy levels, and so on.
Upon measurement, the qubit loses its superposition and irreversibly
collapses into one of the two basis states, either |0> or |1>. Which
of the two states it ends up in may not be deterministic, but can be
determined from the readout of the measurement. The measurement
result is a classical bit, 0 or 1, corresponding to |0> and |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
is a fundamental feature of a quantum mechanical system [Aspect81].
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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 controlled-NOT, or CNOT, gate. The CNOT gate takes as input
two qubits, a control and target, and applies the NOT gate to the
target if the control qubit is set. The truth table looks like
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+====+=====+
| IN | OUT |
+====+=====+
| 00 | 00 |
+----+-----+
| 01 | 01 |
+----+-----+
| 10 | 11 |
+----+-----+
| 11 | 10 |
+----+-----+
Table 1
Now, consider performing a CNOT gate on the state with the first
qubit being the control. We apply a two-qubit gate on all the
superposition states:
CNOT (|00> + |10>)/sqrt(2) -> (|00> + |11>)/sqrt(2).
What is so interesting about this two-qubit gate operation? The
final state is *entangled*. There is no possible way of representing
that quantum state as a product of two individual qubits; they are no
longer independent and the behaviour of either qubit cannot be fully
described without accounting for the other qubit. The states of the
two individual qubits are now correlated beyond what is possible to
achieve classically. Neither qubit is in a definite |0> or |1>
state, but if we perform a measurement on either one, the outcome of
the partner qubit will *always* yield the exact same outcome. The
final state, whether it's |00> or |11>, is fundamentally random as
before, but the states of the two qubits following a measurement will
always be identical.
Once a measurement is performed, the two qubits are once again
independent. The final state is either |00> or |11> and both of
these states can be trivially decomposed into a product of two
individual qubits. The entanglement has been consumed and the
entangled state must be prepared again.
3. Entanglement as the fundamental resource
Entanglement is the fundamental building block of quantum networks.
Consider the state from the previous section:
(|00> + |11>)/sqrt(2).
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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 [Bennett14]
[Ekert91], blind quantum computation [Fitzsimons17], or distributed
quantum computation [Crepeau02].
Entanglement has two very special features from which one can derive
some intuition about the types of applications enabled by a quantum
network.
The first stems from the fact that entanglement enables stronger than
classical correlations, leading to opportunities for tasks that
require coordination. As a trivial example, consider the problem of
consensus between two nodes who want to agree on the value of a
single bit. They can use the quantum network to prepare the state
(|00> + |11>)/sqrt(2) with each node holding one of the two qubits.
Once either of the two nodes performs a measurement, the state of the
two qubits collapses to either |00> or |11>, so whilst the outcome is
random and does not exist before measurement, the two nodes will
always measure the same value. We can also build the more general
multi-qubit state (|00...> + |11...>)/sqrt(2) and perform the same
algorithm between an arbitrary number of nodes. These stronger than
classical correlations generalise to more complicated measurement
schemes as well.
The second feature of entanglement is that it cannot be shared, in
the sense that if two qubits are maximally entangled with each other,
then it is physically impossible for any other system to have any
share of this entanglement [Terhal04]. Hence, entanglement forms a
sort of private and inherently untappable connection between two
nodes once established.
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Entanglement is created through local interactions between two qubits
or as a product of the way the qubits were created (e.g. entangled
photon pairs). To create a distributed entangled state, one can then
physically send one of the qubits to a remote node. It is also
possible to directly entangle qubits that are physically separated,
but this still requires local interactions between some other qubits
that the separated qubits are initially entangled with. Therefore,
it is the transmission of qubits that draws the line between a
genuine quantum network and a collection of quantum computers
connected over a classical network.
A quantum network is defined as a collection of nodes that is able to
exchange qubits and distribute entangled states amongst themselves.
A quantum node that is able only to communicate classically with
another quantum node is not a member of a quantum network.
More complex services and applications can be built on top of
entangled states distributed by the network, see e.g. [ZOO]
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. Sending qubits over a
wire like we send classical bits is simply not as easy to do. There
are several technological as well as fundamental challenges that make
classical approaches unsuitable in a quantum context.
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. Nevertheless, quantum error detection and correction
schemes exist that take this problem into account and how a network
chooses to manage errors will have an impact on its architecture.
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4.1.2. No-cloning theorem
Since directly reading the state of a qubit is not possible, one
could ask if we can simply copy a qubit without looking at it.
Unfortunately, this is fundamentally not possible in quantum
mechanics [Park70] [Wootters82].
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 error
detection and correction mechanisms. Since we cannot read or copy a
quantum state error detection and correction is more involved.
To describe the quality of a quantum state, a physical quantity
called fidelity is used [NielsenChuang]. Fidelity takes a value
between 0 and 1 -- higher is better, and less than 0.5 means the
state is unusable. It measures how close a quantum state is to the
state we have tried to create. It expresses the probability that one
state will pass a test to identify as the other. Fidelity is an
important property of a quantum system that allows us to quantify how
much a particular state has been affected by noise from various
sources (gate errors, channel losses, environment noise).
Interestingly, quantum applications do not need perfect fidelity to
be able to execute -- as long as the fidelity is above some
application-specific threshold, they will simply operate at lower
rates. Therefore, rather than trying to ensure that we always
deliver perfect states (a technologically challenging task)
applications will specify a minimum threshold for the fidelity and
the network will try its best to deliver it. A higher fidelity can
be achieved by either having hardware produce states of better
fidelity (sometimes one can sacrifice rate for higher fidelity) or by
employing quantum error detection and correction mechanisms.
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4.1.4. Inadequacy of direct transmission
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 (Section 4.4.3.2) 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 [Jiang09] [Fowler10] [Devitt13]
[Mural16]. 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 [Briegel98].
4.2. Bell pairs
Bell pair states are the entangled two-qubit states:
|00> + |11>, |00> - |11>, |01> + |10>, |01> - |10>,
where the constant 1/sqrt(2) normalisation factor has been ignored
for clarity. Any of the four Bell pair states above will do, as it
is possible to transform any Bell pair into another Bell pair with
local operations performed on only one of the qubits. When each
qubit in a Bell pair is held by a separate node, either node can
apply a series of single qubit gates to their qubit alone in order to
transform the state between the different variants.
Distributing a Bell pair between two nodes is much easier than
transmitting an arbitrary quantum state over a network. Since the
state is known, handling errors becomes easier and small-scale error-
correction (such as entanglement distillation discussed in a later
section) combined with reattempts becomes a valid strategy.
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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. 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 [Bennett93]. Quantum state teleportation consumes an
unknown qubit state that we want to transmit and recreates it at the
desired destination. This does not violate the no-cloning theorem as
the original state is destroyed in the process.
To achieve this, an entangled pair needs to be distributed between
the source and destination before teleportation commences. The
source then entangles the transmission qubit with its end of the pair
and performs a read out of the two qubits (the sum of these
operations is called a Bell state measurement). This consumes the
Bell pair's entanglement, turning the source and destination qubits
into independent states. The measurements yields two classical bits
which the source sends to the destination over a classical channel.
Based on the value of the received two classical bits, the
destination performs one of four possible corrections (called the
Pauli corrections) on its end of the pair, which turns it into the
unknown qubit state that we wanted to transmit. This requirement to
communicate the measurement read out over a classical channel
unfortunately means that entanglement cannot be used to transmit
information faster than the speed of light.
The unknown quantum state that was transmitted was never fed into the
network itself. Therefore, the network needs to only be able to
reliably produce Bell pairs between any two nodes in the network.
Thus, a key difference between a classical and quantum data planes is
that a classical one carries user data, but a quantum data plane
provides the resources for the user to transmit user data themselves
without further involvement of the network.
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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 their two qubits are delivered to the end-
points.
4.4.1. Elementary link generation
In a quantum network, entanglement is always first generated locally
(at a node or an auxiliary element) followed by a movement of one or
both of the entangled qubits across the link through quantum
channels. In this context, photons (particles of light) are the
natural candidate for entanglement carriers, called flying qubits.
The rationale for this choice is related to the advantages provided
by photons such as moderate interaction with the environment leading
to moderate decoherence, convenient control with standard optical
components, and high-speed, low-loss transmissions. However, since
photons are hard to store, a transducer must transfer the flying
qubit's state to a qubit suitable for information processing and/or
storage (often referred to as a matter qubit).
Since this process may fail, in order to generate and store
entanglement efficiently, we must be able to distinguish successful
attempts from failures. Entanglement generation schemes that are
able to announce successful generation are called heralded
entanglement generation schemes.
There exist three basic schemes for heralded entanglement generation
on a link through coordinated action of the two nodes at the two ends
of the link [Cacciapuoti19]:
* "At mid-point": in this scheme an entangled photon pair source
sitting midway between the two nodes with matter qubits sends an
entangled photon through a quantum channel to each of the nodes.
There, transducers are invoked to transfer the entanglement from
the flying qubits to the matter qubits. In this scheme, the
transducers know if the transfers succeeded and are able to herald
successful entanglement generation via a message exchange over the
classical channel.
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* "At source": in this scheme one of the two nodes sends a flying
qubit that is entangled with one of its matter qubits. A
transducer at the other end of the link will transfer the
entanglement from the flying qubit to one of its matter qubits.
Just like in the previous scheme, the transducer knows if its
transfer succeeded and is able to herald successful entanglement
generation with a classical message sent to the other node.
* "At both end-points": in this scheme both nodes send a flying
qubit that is entangled with one of their matter qubits. A
detector somewhere in between the nodes performs a joint
measurement on the two qubits, which stochastically projects the
remote matter qubits into an entangled quantum state. The
detector knows if the entanglement succeeded and is able to herald
successful entanglement generation by sending a message to each
node over the classical channel.
The "mid-point source" scheme is more robust to photon loss, but in
the other schemes the nodes retain greater control over the entangled
pair generation.
Note that whilst photons travel in a particular direction through the
quantum channel the resulting entangled pair of qubits does not have
a direction associated with it. Physically, there is no upstream or
downstream end of the pair.
4.4.2. Entanglement swapping
The problem with generating entangled pairs directly across a link is
that efficiency decreases with channel length. Beyond a few 10s of
kilometres in optical fibre or 1000 kilometres in free space (via
satellite) the rate is effectively zero and due to the no-cloning
theorem we cannot simply amplify the signal. The solution is
entanglement swapping [Briegel98].
A Bell pair between any two nodes in the network can be constructed
by combining the pairs generated along each individual link on a path
between the two end-points. Each node along the path can consume the
two pairs on the two links that it is connected to in order to
produce a new entangled pair between the two remote ends. This
process is known as entanglement swapping. Pictorially it can be
represented as follows:
+---------+ +---------+ +---------+
| A | | B | | C |
| |------| |------| |
| X1~~~~~~~~~~X2 Y1~~~~~~~~~~Y2 |
+---------+ +---------+ +---------+
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where X1 and X2 are the qubits of the entangled pair X and Y1 and Y2
are the qubits of entangled pair Y. The entanglement is denoted with
~~. In the diagram above, nodes A and B share the pair X and nodes B
and C share the pair Y, but we want entanglement between A and C.
To achieve this goal, we simply teleport the qubit X2 using the pair
Y. This requires node B to perform a Bell state measurement on the
qubits X2 and Y1 which result in the destruction of the entanglement
between Y1 and Y2. However, X2 is recreated in Y2's place, carrying
with it its entanglement with X1. The end-result is shown below:
+---------+ +---------+ +---------+
| 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.
This process of teleporting Bell pairs using other entangled pairs is
called entanglement swapping. Quantum nodes that create long-
distance entangled pairs via entanglement swapping are called quantum
repeaters in academic literature [Briegel98] and we will use the same
terminology in this memo.
4.4.3. Error Management
4.4.3.1. 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 (sometimes also referred
to as purification) [Dur07].
To distil a quantum state, a second (and sometimes third) quantum
state is used as a "test tool" to test a proposition about the first
state, e.g., "the parity of the two qubits in the first state is
even." When the test succeeds, confidence in the state is improved,
and thus the fidelity is improved. The test tool states are
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destroyed in the process, so resource demands increase substantially
when distillation is used. When the test fails, the tested state
must also be discarded. Distillation makes low demands on fidelity
and resources compared to quantum error correction, but distributed
protocols incur round-trip delays due to classical communication
[Bennett96].
4.4.3.2. Quantum Error Correction
Just like classical error correction, quantum error correction (QEC)
encodes logical qubits using several physical (raw) qubits to protect
them from errors described in Section 4.1.3 [Jiang09] [Fowler10]
[Devitt13] [Mural16]. Furthermore, similarly to its classical
counterpart, QEC can not only correct state errors but also account
for lost qubits. Additionally, if all physical qubits which encode a
logical qubit are located at the same node, the correction procedure
can be executed locally, even if the logical qubit is entangled with
remote qubits.
Although QEC was originally a scheme proposed to protect a qubit from
noise, QEC can also be applied to entanglement distillation. Such
QEC-applied distillation is cost-effective but requires a higher base
fidelity.
4.4.3.3. Error management schemes
Quantum networks have been categorized into three "generations" based
on the error management scheme they employ [Mural16]. Note that
these "generations" are more like categories; they do not necessarily
imply a time progression and do not obsolete each other, though the
later generations do require more advanced technologies. Which
generation is used depends on the hardware platform and network
design choices.
Table 2 summarises the generations.
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+===========+=================+=======================+============+
| | First | Second generation | Third |
| | generation | | generation |
+===========+=================+=======================+============+
| Loss | Heralded | Heralded entanglement | Quantum |
| tolerance | entanglement | generation (bi- | Error |
| | generation (bi- | directional classical | Correction |
| | directional | signaling) | (no |
| | classical | | classical |
| | signaling) | | signaling) |
+-----------+-----------------+-----------------------+------------+
+-----------+-----------------+-----------------------+------------+
| Error | Entanglement | Entanglement | Quantum |
| tolerance | distillation | distillation (uni- | Error |
| | (bi-directional | directional classical | Correction |
| | classical | signaling) or Quantum | (no |
| | signaling) | Error Correction (no | classical |
| | | classical signaling) | signaling) |
+-----------+-----------------+-----------------------+------------+
Table 2: Classical signaling and generations
Generations are defined by the directions of classical signalling
required in their distributed protocols for loss tolerance and error
tolerance. Classical signalling carries the classical bits and
incurs round-trip delays described in Section 4.4.3.1, hence they
affect the performance of quantum networks, especially as the
distance between the communicating nodes increases.
Loss tolerance is about tolerating qubit transmission losses between
nodes. Heralded entanglement generation, as described in
Section 4.4.1, confirms the receipt of an entangled qubit using a
heralding signal. A pair of directly connected quantum nodes
repeatedly attempt to generate an entangled pair until the a
heralding signal is received. As described in Section 4.4.3.2, QEC
can be applied to complement lost qubits eliminating the need for re-
attempts. Furthermore, since the correction procedure is composed of
local operations, it does not require a heralding signal. However,
it is possible only when the photon loss rate from transmission to
measurement is less than 50%.
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Error tolerance is about tolerating quantum state errors.
Entanglement distillation is the easiest mechanism for improved error
tolerance to implement, but it incurs round-trip delays due the
requirement for bi-directional classical signalling. The
alternative, QEC, is able to correct state errors locally so that it
does not need any classical signalling between the quantum nodes. In
between these two extremes, there is also QEC-applied distillation,
which requires uni-directional classical signalling.
The three "generations" summarised:
1. First generation quantum networks use heralding for loss
tolerance and entanglement distillation for error tolerance.
These networks can be implemented even with a limited set of
available quantum gates.
2. Second generation quantum networks improve upon the first
generation with QEC codes for error tolerance (but not loss
tolerance). At first, QEC will be applied to entanglement
distillation only which requires uni-directional classical
signalling. Later, QEC codes will be used to create logical Bell
pairs which no longer require any classical signalling for the
purposes of error tolerance. Heralding is still used to
compensate for transmission losses.
3. Third generation quantum networks directly transmit QEC encoded
qubits to adjacent nodes, as discussed in Section 4.1.4.
Elementary link Bell pairs can now be created without heralding
or any other classical signalling. Furthermore, this also
enables direct transmission architectures in which qubits are
forwarded end-to-end like classical packets rather than relying
on Bell pairs and entanglement swapping.
4.4.4. Delivery
Eventually, the Bell pairs must be delivered to an application (or
higher layer protocol) at the two end-nodes. A detailed list of such
requirements is beyond the scope of this memo. At minimum, the end-
nodes require information to map a particular Bell pair to the qubit
in their local memory that is part of this entangled pair.
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.
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5.1. Challenges
This subsection covers the major fundamental challenges building
quantum networks. Here, we only describe the fundamental
differences. Technological limitations are described later.
1. Bell pairs are not equivalent to payload carrying packets.
In most classical networks, including Ethernet, Internet Protocol
(IP), and Multi-Protocol Label Switching (MPLS) networks, user
data is grouped into packets. In addition to the user data, each
packet also contains a series of headers which contain the
control information that lets routers and switches forward it
towards its destination. Packets are the fundamental unit in a
classical network.
In a quantum network, the entangled pairs of qubits are the basic
unit of networking. These qubits themselves do not carry any
headers. Therefore, quantum networks will have to send all
control information via separate classical channels which the
repeaters will have to correlate with the qubits stored in their
memory.
2. "Store and forward" vs "store and swap" quantum networks.
As described in Section 4.4.1, quantum links provide Bell pairs
that are undirected network resources, in contrast to directed
frames of classical networks. This phenomenological distinction
leads to architectural differences between quantum networks and
classical networks. Quantum networks combine multiple elementary
link Bell pairs together to create one an end-to-end Bell pair,
whereas classical networks deliver messages from one end to the
other end hop by hop.
Classical networks receive data on one interface, store it in
local buffers, then forward the data to another appropriate
interface. Quantum networks store Bell pairs and then execute
entanglement swapping instead of forwarding in the data plane.
Such quantum networks are "store and swap" networks. In "store
and swap" networks, we do not need to care about the order in
which the Bell pairs were generated since they are undirected.
This distinction makes control algorithms and optimisation of
quantum networks different from classical ones. Note that third
generation quantum networks, as described in Section 4.4.1, will