Internet Research Task Force (IRTF) W. Kozlowski
Request for Comments: 9340 S. Wehner
Category: Informational QuTech
ISSN: 2070-1721 R. Van Meter
Keio University
B. Rijsman
Individual
A. S. Cacciapuoti
M. Caleffi
University of Naples Federico II
S. Nagayama
Mercari, Inc.
March 2023
Architectural Principles for a Quantum Internet
Abstract
The vision of a quantum internet is to enhance existing 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 quantum entanglement
networks have been realised, but there is no practical proposal for
how to organise, utilise, and manage such networks. In this
document, 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. It is also
intended to provide a foundation for discussion between physicists
and network specialists. This document is a product of the Quantum
Internet Research Group (QIRG).
Status of This Memo
This document is not an Internet Standards Track specification; it is
published for informational purposes.
This document is a product of the Internet Research Task Force
(IRTF). The IRTF publishes the results of Internet-related research
and development activities. These results might not be suitable for
deployment. This RFC represents the consensus of the Quantum
Internet Research Group of the Internet Research Task Force (IRTF).
Documents approved for publication by the IRSG are not candidates for
any level of Internet Standard; see Section 2 of RFC 7841.
Information about the current status of this document, any errata,
and how to provide feedback on it may be obtained at
https://www.rfc-editor.org/info/rfc9340.
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Copyright (c) 2023 IETF Trust and the persons identified as the
document authors. All rights reserved.
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Table of Contents
1. Introduction
2. Quantum Information
2.1. Quantum State
2.2. Qubit
2.3. Multiple Qubits
3. Entanglement as the Fundamental Resource
4. Achieving Quantum Connectivity
4.1. Challenges
4.1.1. The Measurement Problem
4.1.2. No-Cloning Theorem
4.1.3. Fidelity
4.1.4. Inadequacy of Direct Transmission
4.2. Bell Pairs
4.3. Teleportation
4.4. The Life Cycle of Entanglement
4.4.1. Elementary Link Generation
4.4.2. Entanglement Swapping
4.4.3. Error Management
4.4.4. Delivery
5. Architecture of a Quantum Internet
5.1. Challenges
5.2. Classical Communication
5.3. Abstract Model of the Network
5.3.1. The Control Plane and the Data Plane
5.3.2. Elements of a Quantum Network
5.3.3. Putting It All Together
5.4. Physical Constraints
5.4.1. Memory Lifetimes
5.4.2. Rates
5.4.3. Communication Qubits
5.4.4. Homogeneity
6. Architectural Principles
6.1. Goals of a Quantum Internet
6.2. The Principles of a Quantum Internet
7. A Thought Experiment Inspired by Classical Networks
8. Security Considerations
9. IANA Considerations
10. Informative References
Acknowledgements
Authors' Addresses
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
to form an overall hybrid classical-quantum network supporting new
capabilities that are otherwise impossible to realise [VanMeterBook].
For example, the most well-known application of quantum
communication, Quantum Key Distribution (QKD) [QKD], can create and
distribute a pair of symmetric encryption keys in such a way that the
security of the entire process relies on the laws of physics (and
thus can be mathematically proven to be unbreakable) rather than the
intractability of certain mathematical problems [Bennett14]
[Ekert91]. Small networks capable of QKD have even already been
deployed at short (roughly 100-kilometre) distances [Elliott03]
[Peev09] [Aguado19] [Joshi20].
The quantum networking paradigm also offers promise for a range of
new applications beyond quantum cryptography, such as distributed
quantum computation [Cirac99] [Crepeau02]; secure quantum computing
in the cloud [Fitzsimons17]; quantum-enhanced measurement networks
[Giovannetti04]; or higher-precision, long-baseline telescopes
[Gottesman12]. These applications are much more demanding than QKD,
and networks capable of executing them are in their infancy. The
first fully quantum, multinode network capable of sending, receiving,
and manipulating distributed quantum information has only recently
been realised [Pompili21.1].
Whilst a lot of effort has gone into physically realising and
connecting such devices, and making improvements to their speed and
error tolerance, no proposals for how to run these networks have been
worked out at the time of this writing. 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 directly by using low-level, custom-built, and
hardware-specific interfaces, rather than being managed by a network
stack that exposes a convenient high-level interface, such as
sockets. Only recently was the first-ever attempt at such a network
stack experimentally demonstrated in a laboratory setting
[Pompili21.2]. Furthermore, whilst physical mechanisms for
transmitting quantum information exist, there are no robust protocols
for managing such transmissions.
This document, produced by the Quantum Internet Research Group
(QIRG), introduces quantum networks and presents general guidelines
for the design and construction of such networks. Overall, it is
intended as an introduction to the subject for network engineers and
researchers. It should not be considered as a conclusive statement
on how quantum networks should or will be implemented. This document
was discussed on the QIRG mailing list and several IETF meetings. It
represents the consensus of the QIRG members, of both experts in the
subject matter (from the quantum and networking domains) and
newcomers who are the target audience.
2. Quantum Information
In order to understand the framework for quantum networking, a basic
understanding of quantum information theory is necessary. The
following sections aim to introduce the minimum amount of knowledge
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 the reader to
[SutorBook] and [NielsenChuang] for an in-depth introduction to
quantum information systems.
2.1. Quantum State
A quantum mechanical system is described by its quantum state. A
quantum state is an abstract object that provides a complete
description of the system at that particular moment. When combined
with the rules of the system's evolution in time, such as a quantum
circuit, it also then provides a complete description of the system
at all times. For the purposes of computing and networking, the
classical equivalent of a quantum state would be a string or stream
of logical bit values. These bits provide a complete description of
what values we can read out from that string at that particular
moment, and when combined with its rules for evolution in time, such
as a logical circuit, we will also know its value at any other time.
Just like a single classical bit, a quantum mechanical system can be
simple and consist of a single particle, e.g., an atom or a photon of
light. In this case, the quantum state provides the complete
description of that one particle. Similarly, just like a string of
bits consists of multiple bits, a single quantum state can be used to
also describe an ensemble of many particles. However, because
quantum states are governed by the laws of quantum mechanics, their
behaviour is significantly different to that of a string of bits. In
this section, we will summarise the key concepts to understand these
differences. We will then explain their consequences for networking
in the rest of this document.
2.2. 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, its state can exist
in a superposition of the two possibilities:
|qubit⟩ = a |0⟩ + b |1⟩,
where |X⟩ is Dirac's ket notation for a quantum state (the value that
a qubit holds) -- 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; 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].
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⟩.
It is important to note that "qubit" can have two meanings. In the
first meaning, "qubit" refers to a physical quantum *system* whose
quantum state can be expressed as a superposition of two basis
states, which we often label |0⟩ and |1⟩. Here, "qubit" refers to a
physical implementation akin to what a flip-flop, switch, voltage, or
current would be for a classical bit. In the second meaning, "qubit"
refers to the abstract quantum *state* of a quantum system with such
two basis states. In this case, the meaning of "qubit" is akin to
the logical value of a bit, from classical computing, i.e., "logical
0" or "logical 1". The two concepts are related, because a physical
"qubit" (first meaning) can be used to store the abstract "qubit"
(second meaning). Both meanings are used interchangeably in
literature, and the meaning is generally clear from the context.
2.3. 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).
The constant 1/sqrt(2) is called the normalisation factor and
reflects the fact that the probabilities of measuring either a |0⟩ or
a |1⟩ for the first qubit add up to one.
Let us now consider the two-qubit Controlled NOT, or CNOT, gate. The
CNOT gate takes as input two qubits -- a control and a 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 |
+----+-----+
Table 1: CNOT Truth Table
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. That is, it is not possible to describe the
quantum state of either of the individual qubits in a way that is
independent of the other qubit. Only the quantum state of the system
that consists of both qubits provides a physically complete
description of the two-qubit system. 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. One can think of this as flipping two coins,
but both coins always land on "heads" or both land on "tails"
together -- something that we know is impossible classically.
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).
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 measurement schemes that are
more complicated 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 these two qubits to also be
entangled with a third qubit [Terhal04]. Hence, entanglement forms a
sort of private and inherently untappable connection between two
nodes once established.
Entanglement is created through local interactions between two qubits
or as a product of the way the qubits were created (e.g., entangled
photon pairs). To create a distributed entangled state, one can then
physically send one of the qubits to a remote node. It is also
possible to directly entangle qubits that are physically separated,
but this still requires local interactions between some other qubits
that the separated qubits are initially entangled with. Therefore,
it is the transmission of qubits that draws the line between a
genuine quantum network and a collection of quantum computers
connected over a classical network.
A quantum network is defined as a collection of nodes that is able to
exchange qubits and distribute entangled states amongst themselves.
A quantum node that is able only to communicate classically with
another quantum node is not a member of a quantum network.
Services and applications that are more complex can be built on top
of entangled states distributed by the network; for example, see
[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.
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 are 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 the
state will behave exactly the same as our desired state. 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
employing quantum error detection and correction mechanisms (see
[Mural16] and Chapter 11 of [VanMeterBook]).
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 (QEC) (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, QEC makes very high demands on both
resources (physical qubits needed) and their initial fidelity.
Implementation is very challenging, and QEC is not expected to be
used until later generations of quantum networks are possible (see
Figure 2 of [Mural16] and Section 4.4.3.3 of this document). Until
then, quantum networks rely on entanglement swapping (Section 4.4.2)
and teleportation (Section 4.3). This 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, as discussed in
Section 4.4.3.1), combined with reattempts, becomes a valid strategy.
The reason for using Bell pairs specifically as opposed to any other
two-qubit state is that they are the maximally entangled two-qubit
set of basis states. Maximal entanglement means that these states
have the strongest non-classical correlations of all possible two-
qubit states. Furthermore, since single-qubit local operations can
never increase entanglement, states that are less entangled 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 readout 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 measurement 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 readout 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 data plane and a quantum
data plane is that a classical data plane 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.
4.4. The Life Cycle of Entanglement
Reducing the problem of quantum connectivity to one of generating a
Bell pair has reduced the problem to a simpler, more fundamental
case, 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. Because these photons
carry quantum states from place to place at high speed, we call them
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.
"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
flying 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 tens 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 to which it is connected, in order to
produce a new entangled pair between the two remote ends. This
process is known as entanglement swapping. It can be represented
pictorially 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 perform a Bell state measurement on the
qubits X2 and Y1 that results 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 readout 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]. We will use the same
terminology in this document.
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
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 QEC, but distributed protocols incur round-
trip delays due to classical communication [Bennett96].
4.4.3.2. Quantum Error Correction (QEC)
Just like classical error correction, QEC encodes logical qubits
using several physical (raw) qubits to protect them from the 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 that 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 categorised 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 technologies that are more advanced.
Which generation is used depends on the hardware platform and network
design choices.
Table 2 summarises the generations.
+===========+================+=======================+=============+
| | First | Second generation | Third |
| | generation | | generation |
+===========+================+=======================+=============+
| Loss | Heralded | Heralded entanglement | QEC (no |
| tolerance | entanglement | generation | classical |
| | generation | (bidirectional | signalling) |
| | (bidirectional | classical signalling) | |
| | classical | | |
| | signalling) | | |
+-----------+----------------+-----------------------+-------------+
+-----------+----------------+-----------------------+-------------+
| Error | Entanglement | Entanglement | QEC (no |
| tolerance | distillation | distillation | classical |
| | (bidirectional | (unidirectional | signalling) |
| | classical | classical signalling) | |
| | signalling) | or QEC (no classical | |
| | | signalling) | |
+-----------+----------------+-----------------------+-------------+
Table 2: Classical Signalling 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,
incurring round-trip delays. As described in Section 4.4.3.1, these
delays 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 heralding
signal is received. As described in Section 4.4.3.2, QEC can be
applied to complement lost qubits, eliminating the need for
reattempts. 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%.
Error tolerance is about tolerating quantum state errors.
Entanglement distillation is the easiest mechanism to implement for
improved error tolerance, but it incurs round-trip delays due to the
requirement for bidirectional 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
unidirectional 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 unidirectional classical
signalling. Later, QEC codes will be used to create logical Bell
pairs that 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.
Despite the fact that there are important distinctions in how errors
will be managed in the different generations, it is unlikely that all
quantum networks will consistently use the same method. This is due
to different hardware requirements of the different generations and
the practical reality of network upgrades. Therefore, it is
unavoidable that eventually boundaries between different error
management schemes start forming. This will affect the content and
semantics of messages that must cross those boundaries -- for both
connection setup and real-time operation [Nagayama16].
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 document. 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.
5.1. Challenges
This subsection covers the major fundamental challenges involved in
building quantum networks. Here, we only describe the fundamental
differences. Technological limitations are described in Section 5.4.
1. Bell pairs are not equivalent to packets that carry payload.
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 that 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. Furthermore, unlike a classical packet, which is located
at a single node, a Bell pair consists of two qubits distributed
across two nodes. This has a fundamental impact on how quantum
networks will be managed and how protocols need to be designed.
To make long-distance Bell pairs, the nodes may have to keep
their qubits in their quantum memories and wait until control
information is exchanged before proceeding with the next
operation. This signalling will result in additional latency,
which will depend on the distance between the nodes holding the
two ends of the Bell pair. Error management, such as
entanglement distillation, is a typical example of such control
information exchange [Nagayama21] (see also Section 4.4.3.3).
2. "Store and forward" and "store and swap" quantum networks require
different state management techniques.
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 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, and 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.
However, whilst the ordering does not matter, it is very
important that the right entangled pairs get swapped, and that
the intermediate measurement outcomes (see Section 4.4.2) are
signalled to and correlated with the correct qubits at the other
nodes. Otherwise, the final end-to-end entangled pair will not
be created between the expected end-points or will be in a
different quantum state than expected. For example, rather than
Alice receiving a qubit that is entangled with Bob's qubit, her
qubit is entangled with Charlie's qubit. This distinction makes
control algorithms and optimisation of quantum networks different
from those for classical networks, in the sense that swapping is
stateful in contrast to stateless packet-by-packet forwarding.
Note that, as described in Section 4.4.3.3, third-generation
quantum networks will be able to support a "store and forward"
architecture in addition to "store and swap".
3. An entangled pair is only useful if the locations of both qubits
are known.
A classical network packet logically exists only at one location
at any point in time. If a packet is modified in some way,
whether headers or payload, this information does not need to be
conveyed to anybody else in the network. The packet can be
simply forwarded as before.
In contrast, entanglement is a phenomenon in which two or more
qubits exist in a physically distributed state. Operations on
one of the qubits change the mutual state of the pair. Since the
owner of a particular qubit cannot just read out its state, it
must coordinate all its actions with the owner of the pair's
other qubit. Therefore, the owner of any qubit that is part of
an entangled pair must know the location of its counterpart.
Location, in this context, need not be the explicit spatial
location. A relevant pair identifier, a means of communication
between the pair owners, and an association between the pair ID
and the individual qubits will be sufficient.
4. Generating entanglement requires temporary state.
Packet forwarding in a classical network is largely a stateless
operation. When a packet is received, the router does a lookup
in its forwarding table and sends the packet out of the
appropriate output. There is no need to keep any memory of the
packet any more.
A quantum node must be able to make decisions about qubits that
it receives and is holding in its memory. Since qubits do not
carry headers, the receipt of an entangled pair conveys no
control information based on which the repeater can make a
decision. The relevant control information will arrive
separately over a classical channel. This implies that a
repeater must store temporary state, as the control information
and the qubit it pertains to will, in general, not arrive at the
same time.
5.2. Classical Communication
In this document, we have already covered two different roles that
classical communication must perform the following:
* Communicate classical bits of information as part of distributed
protocols such as entanglement swapping and teleportation.
* Communicate control information within a network, including
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 limits). Therefore, quantum nodes will need to manage two
data planes in parallel: a classical data plane and a quantum data
plane. Additionally, a node must be able to correlate information
between the two planes so that the control information received on a
classical channel can be applied to the qubits managed by the quantum
data plane.
5.3. Abstract Model of the Network
5.3.1. The Control Plane and the Data Plane
Control plane protocols for quantum networks will have many
responsibilities similar to their classical counterparts, namely
discovering the network topology, resource management, populating
data plane tables, etc. Most of these protocols do not require the
manipulation of quantum data and can operate simply by exchanging
classical messages only. There may also be some control plane
functionality that does require the handling of quantum data
[QI-Scenarios]. As it is not clear if there is much benefit in
defining a separate quantum control plane given the significant
overlap in responsibilities with its classical counterpart, the
question of whether there should be a separate quantum control plane
is beyond the scope of this document.
However, the data plane separation is much more distinct, and there
will be two data planes: a classical data plane and a quantum data
plane. The classical data plane processes and forwards classical
packets. The quantum data plane processes and swaps entangled pairs.
Third-generation quantum networks may also forward qubits in addition
to swapping Bell pairs.
In addition to control plane messages, there will also be control
information messages that operate at the granularity of individual
entangled pairs, such as heralding messages used for elementary link
generation (Section 4.4.1). In terms of functionality, these
messages are closer to classical packet headers than control plane
messages, and thus we consider them to be part of the quantum data
plane. Therefore, a quantum data plane also includes the exchange of
classical control information at the granularity of individual qubits
and entangled pairs.
5.3.2. Elements of a Quantum Network
We have identified quantum repeaters as the core building block of a
quantum network. However, a quantum repeater will have to do more
than just entanglement swapping in a functional quantum network. Its
key responsibilities will include the following:
1. Creating link-local entanglement between neighbouring nodes.
2. Extending entanglement from link-local pairs to long-range pairs
through entanglement swapping.
3. Performing distillation to manage the fidelity of the produced
pairs.
4. Participating in the management of the network (routing, etc.).
Not all quantum repeaters in the network will be the same; here, we
break them down further:
Quantum routers (controllable quantum nodes): A quantum router is a
quantum repeater with a control plane that participates in the
management of the network and will make decisions about which
qubits to swap to generate the requested end-to-end pairs.
Automated quantum nodes: An automated quantum node is a data-plane-
only quantum repeater that does not participate in the network
control plane. Since the no-cloning theorem precludes the use of
amplification, long-range links will be established by chaining
multiple such automated nodes together.
End nodes: End nodes in a quantum network must be able to receive
and handle an entangled pair, but they do not need to be able to
perform an entanglement swap (and thus are not necessarily quantum
repeaters). End nodes are also not required to have any quantum
memory, as certain quantum applications can be realised by having
the end node measure its qubit as soon as it is received.
Non-quantum nodes: Not all nodes in a quantum network need to have a
quantum data plane. A non-quantum node is any device that can
handle classical network traffic.
Additionally, we need to identify two kinds of links that will be
used in a quantum network:
Quantum links: A quantum link is a link that can be used to generate
an entangled pair between two directly connected quantum
repeaters. This may include additional mid-point elements as
described in Section 4.4.1. It may also include a dedicated
classical channel that is to be used solely for the purpose of
coordinating the entanglement generation on this quantum link.
Classical links: A classical link is a link between any node in the
network that is capable of carrying classical network traffic.
Note that passive elements, such as optical switches, do not destroy
the quantum state. Therefore, it is possible to connect multiple
quantum nodes with each other over an optical network and perform
optical switching rather than routing via entanglement swapping at
quantum routers. This does require coordination with the elementary
link entanglement generation process, and it still requires repeaters
to overcome the short-distance limitations. However, this is a
potentially feasible architecture for local area networks.
5.3.3. Putting It All Together
A two-hop path in a generic quantum network can be represented as
follows:
+-----+ +-----+
| App |- - - - - - - - - -CC- - - - - - - - - -| App |
+-----+ +------+ +-----+
| EN |------ CL ------| QR |------ CL ------| EN |
| |------ QL ------| |------ QL ------| |
+-----+ +------+ +-----+
App - user-level application
EN - End Node
QL - Quantum Link
CL - Classical Link
CC - Classical Channel (traverses one or more CLs)
QR - Quantum Repeater
An application (App) running on two End Nodes (ENs) attached to a
network will at some point need the network to generate entangled
pairs for its use. This may require negotiation between the ENs
(possibly ahead of time), because they must both open a communication
end-point that the network can use to identify the two ends of the
connection. The two ENs use a Classical Channel (CC) available in
the network to achieve this goal.
When the network receives a request to generate end-to-end entangled
pairs, it uses the Classical Links (CLs) to coordinate and claim the
resources necessary to fulfill this request. This may be some
combination of prior control information (e.g., routing tables) and
signalling protocols, but the details of how this is achieved are an
active research question. A thought experiment on what this might
look like be can be found in Section 7.
During or after the distribution of control information, the network
performs the necessary quantum operations, such as generating
entanglement over individual Quantum Links (QLs), performing
entanglement swaps at Quantum Repeaters (QRs), and further signalling
to transmit the swap outcomes and other control information. Since
Bell pairs do not carry any user data, some of these operations can
be performed before the request is received, in anticipation of the
demand.
Note that here, "signalling" is used in a very broad sense and covers
many different types of messaging necessary for entanglement
generation control. For example, heralded entanglement generation
requires very precise timing synchronisation between the neighbouring
nodes, and thus the triggering of entanglement generation and
heralding may happen over its own, perhaps physically separate, CL,
as was the case in the network stack demonstration described in
[Pompili21.2]. Higher-level signalling with timing requirements that
are less stringent (e.g., control plane signalling) may then happen
over its own CL.
The entangled pair is delivered to the application once it is ready,
together with the relevant pair identifier. However, being ready
does not necessarily mean that all link pairs and entanglement swaps
are complete, as some applications can start executing on an
incomplete pair. In this case, the remaining entanglement swaps will
propagate the actions across the network to the other end, sometimes
necessitating fixup operations at the EN.
5.4. 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 artifacts of the early stages of a new technology. Here, we
consider a highly abstract scenario and refer to [Wehner18] for
pointers to the physics literature.
5.4.1. 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 in quantum network hardware are, as of
2020, on the order of seconds [Abobeih18], although a lifetime of a
minute has also been demonstrated for qubits not connected to a
quantum network [Bradley19]. These values have increased
tremendously over the lifetime of the different technologies and are
bound to keep increasing. However, if quantum networks are to be
realised in the near future, they need to be able to handle short
memory lifetimes -- for example, by reducing latency on critical
paths.
5.4.2. Rates
Entanglement generation on a link between two connected nodes is not
a very efficient process, and it requires many attempts to succeed
[Hensen15] [Dahlberg19]. For example, the highest achievable rates
of success between nitrogen-vacancy center nodes -- which, in
addition to entanglement generation are also capable of storing and
processing the resulting qubits -- are on the order of 10 Hz.
Combined with short memory lifetimes, this leads to very tight timing
windows to build up network-wide connectivity.
Other platforms have shown higher entanglement rates, but this
usually comes at the cost of other hardware capabilities, such as no
quantum memory and/or limited processing capabilities [Wei22].
Nevertheless, the current rates are not sufficient for practical
applications beyond simple experimental proofs of concept. However,
they are expected to improve over time as quantum network technology
evolves [Wei22].
5.4.3. Communication Qubits
Most physical architectures capable of storing qubits are only able
to generate entanglement using only a subset of available qubits
called communication qubits [Dahlberg19]. 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.
5.4.4. Homogeneity
At present, all existing quantum network implementations are
homogeneous, and they do not interface with each other. In general,
it is very challenging to combine different quantum information
processing technologies.
There are many different physical hardware platforms for implementing
quantum networking hardware. The different technologies differ in
how they store and manipulate qubits in memory and how they generate
entanglement across a link with their neighbours. For example,
hardware based on optical elements and atomic ensembles [Sangouard11]
is very efficient at generating entanglement at high rates but
provides limited processing capabilities once the entanglement is
generated. On the other hand, nitrogen-vacancy-based platforms
[Hensen15] or trapped ion platforms [Moehring07] offer a much greater
degree of control over the qubits but have a harder time generating
entanglement at high rates.
In order to overcome the weaknesses of the different platforms,
coupling the different technologies will help to build fully
functional networks. For example, end nodes may be implemented using
technology with good qubit processing capabilities to enable complex
applications, but automated quantum nodes that serve only to "repeat"
along a linear chain, where the processing logic is much simpler, can
be implemented with technologies that sacrifice processing
capabilities for higher entanglement rates at long distances
[Askarani21].
This point is further exacerbated by the fact that quantum computers
(i.e., end nodes in a quantum network) are often based on different
hardware platforms than quantum repeaters, thus requiring a coupling
(transduction) between the two. This is especially true for quantum
computers based on superconducting technology, which are challenging
to connect to optical networks. However, even trapped ion quantum
computers, which make up a platform that has shown promise for
quantum networking, will still need to connect to other platforms
that are better at creating entanglement at high rates over long
distances (hundreds of kilometres).
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, will work? Furthermore, how do we design networks
so that they work under the constraints imposed by the hardware
available today but do not impose unnecessary burdens on future
technology?
As quantum networking is a completely new technology that is likely
to see many iterations over its lifetime, this document must not
serve as a definitive set of rules but merely as a general set of
recommended guidelines for the first generations of quantum networks
based on principles and observations made by the community. The
benefit of having a community-built document at this early stage is
that expertise in both quantum information and network architecture
is needed in order to successfully build a quantum internet.
6.1. Goals of a Quantum Internet
When outlining any set of principles, we must ask ourselves what
goals we want to achieve, as inevitably trade-offs must be made. So,
what sort of goals should drive a quantum network architecture? The
following list has been inspired by the history of computer
networking, and thus it is inevitably very similar to one that could
be produced for the classical Internet [Clark88]. However, whilst
the goals may be similar, the challenges involved are often
fundamentally different. The list will also most likely evolve with
time and the needs of its users.
1. Support distributed quantum applications.
This goal seems trivially obvious, but it makes a subtle, but
important, point that highlights a key difference between quantum
and classical networks. Ultimately, quantum data transmission is
not the goal of a quantum network -- it is only one possible
component of quantum application protocols that are more advanced
[Wehner18]. Whilst transmission certainly could be used as a
building block for all quantum applications, it is not the most
basic one possible. For example, entanglement-based QKD, the
most well-known quantum application protocol, only relies on the
stronger-than-classical correlations and inherent secrecy of
entangled Bell pairs and does not have to transmit arbitrary
quantum states [Ekert91].
The primary purpose of a quantum internet is to support
distributed quantum application protocols, and it is of utmost
importance that they can run well and efficiently. Thus, it is
important to develop performance metrics meaningful to
applications to drive the development of quantum network
protocols. For example, the Bell pair generation rate is
meaningless if one does not also consider their fidelity. It is
generally much easier to generate pairs of lower fidelity, but
quantum applications may have to make multiple reattempts or even
abort if the fidelity is too low. A review of the requirements
for different known quantum applications can be found in
[Wehner18], and an overview of use cases can be found in
[QI-Scenarios].
2. Support tomorrow's distributed quantum applications.
The only principle of the Internet that should survive
indefinitely is the principle of constant change [RFC1958].
Technical change is continuous, and the size and capabilities of
the quantum internet will change by orders of magnitude.
Therefore, it is an explicit goal that a quantum internet
architecture be able to embrace this change. We have the benefit
of having been witness to the evolution of the classical Internet
over several decades, and we have seen what worked and what did
not. It is vital for a quantum internet to avoid the need for
flag days (e.g., NCP to TCP/IP) or upgrades that take decades to
roll out (e.g., IPv4 to IPv6).
Therefore, it is important that any proposed architecture for
general-purpose quantum repeater networks can integrate new
devices and solutions as they become available. The architecture
should not be constrained due to considerations for early-stage
hardware and applications. For example, it is already possible
to run QKD efficiently on metropolitan-scale networks, and such
networks are already commercially available. However, they are
not based on quantum repeaters and thus will not be able to
easily transition to applications that are more sophisticated.
3. Support heterogeneity.
There are multiple proposals for realising practical quantum
repeater hardware, and they all have their advantages and
disadvantages. Some may offer higher Bell pair generation rates
on individual links at the cost of entanglement swap operations
that are more difficult. Other platforms may be good all around
but are more difficult to build.
In addition to physical boundaries, there may be distinctions in
how errors are managed (Section 4.4.3.3). These differences will
affect the content and semantics of messages that cross these
boundaries -- for both connection setup and real-time operation.
The optimal network configuration will likely leverage the
advantages of multiple platforms to optimise the provided
service. Therefore, it is an explicit goal to incorporate varied
hardware and technology support from the beginning.
4. Ensure security at the network level.
The question of security in quantum networks is just as critical
as it is in the classical Internet, especially since enhanced
security offered by quantum entanglement is one of the key
driving factors.
Fortunately, from an application's point of view, as long as the
underlying implementation corresponds to (or sufficiently
approximates) theoretical models of quantum cryptography, quantum
cryptographic protocols do not need the network to provide any
guarantees about the confidentiality or integrity of the
transmitted qubits or the generated entanglement (though they may
impose requirements on the classical channel, e.g., to be
authenticated [Wang21]). Instead, applications will leverage the
classical networks to establish the end-to-end security of the
results obtained from the processing of entangled qubits.
However, it is important to note that whilst classical networks
are necessary to establish these end-to-end guarantees, the
security relies on the properties of quantum entanglement. For
example, QKD uses classical information reconciliation [Tang19]
for error correction and privacy amplification [Elkouss11] for
generating the final secure key, but the raw bits that are fed
into these protocols must come from measuring entangled qubits
[Ekert91]. In another application, secure delegated quantum
computing, the client hides its computation from the server by
sending qubits to the server and then requesting (in a classical
message) that the server measure them in an encoded basis. The
client then decodes the results it receives from the server to
obtain the result of the computation [Broadbent10]. Once again,
whilst a classical network is used to achieve the goal of secure
computation, the remote computation is strictly quantum.
Nevertheless, whilst applications can ensure their own end-to-end
security, network protocols themselves should be security aware
in order to protect the network itself and limit disruption.
Whilst the applications remain secure, they are not necessarily
operational or as efficient in the presence of an attacker. For
example, if an attacker can measure every qubit between two
parties trying to establish a key using QKD, no secret key can be
generated. Security concerns in quantum networks are described
in more detail in [Satoh17] and [Satoh20].
5. Make them easy to monitor.
In order to manage, evaluate the performance of, or debug a
network, it is necessary to have the ability to monitor the
network while ensuring that there will be mechanisms in place to
protect the confidentiality and integrity of the devices
connected to it. Quantum networks bring new challenges in this
area, so it should be a goal of a quantum network architecture to
make this task easy.
The fundamental unit of quantum information, the qubit, cannot be
actively monitored, as any readout irreversibly destroys its
contents. One of the implications of this fact is that measuring
an individual pair's fidelity is impossible. Fidelity is
meaningful only as a statistical quantity that requires constant
monitoring of generated Bell pairs, achieved by sacrificing some
Bell pairs for use in tomography or other methods.
Furthermore, given one end of an entangled pair, it is impossible
to tell where the other qubit is without any additional classical
metadata. It is impossible to extract this information from the
qubits themselves. This implies that tracking entangled pairs
necessitates some exchange of classical information. This
information might include (i) a reference to the entangled pair
that allows distributed applications to coordinate actions on
qubits of the same pair and (ii) the two bits from each
entanglement swap necessary to identify the final state of the
Bell pair (Section 4.4.2).
6. Ensure availability and resilience.
Any practical and usable network, classical or quantum, must be
able to continue to operate despite losses and failures and be
robust to malicious actors trying to disable connectivity. A
difference between quantum and classical networks is that quantum
networks are composed of two types of data planes (quantum and
classical) and two types of channels (quantum and classical) that
must be considered. Therefore, availability and resilience will
most likely require a more advanced treatment than they do in
classical networks.
Note that privacy, whilst related to security, is not listed as an
explicit goal, because the privacy benefits will depend on the use
case. For example, QKD only provides increased security for the
distribution of symmetric keys [Bennett14] [Ekert91]. The handling,
manipulation, sharing, encryption, and decryption of data will remain
entirely classical, limiting the benefits to privacy that can be
gained from using a quantum network. On the other hand, there are
applications like blind quantum computation, which provides the user
with the ability to execute a quantum computation on a remote server
without the server knowing what the computation was or its input and
output [Fitzsimons17]. Therefore, privacy must be considered on a
per-application basis. An overview of quantum network use cases can
be found in [QI-Scenarios].
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 for 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 [VanMeter13.1] and
[Dahlberg19].
1. Entanglement is the fundamental service.
The key service that a quantum network provides is the
distribution of entanglement between the nodes in a network. All
distributed quantum applications are built on top of this key
resource. Applications such as clustered quantum computing,
distributed quantum computing, distributed quantum sensing
networks, and certain kinds of quantum secure networks all
consume quantum entanglement as a resource. Some applications
(e.g., QKD) simply measure the entangled qubits to obtain a
shared secret key [QKD]. Other applications (e.g., distributed
quantum computing) build abstractions and operations that are
more complex on the entangled qubits, e.g., distributed CNOT
gates [DistCNOT] or teleportation of arbitrary qubit states
[Teleportation].
A quantum network may also distribute multipartite entangled
states (entangled states of three or more qubits) [Meignant19],
which are useful for applications such as conference key
agreement [Murta20], distributed quantum computing [Cirac99],
secret sharing [Qin17], and clock synchronisation [Komar14],
though it is worth noting that multipartite entangled states can
also be constructed from multiple entangled pairs distributed
between the end nodes.
2. Bell pairs are indistinguishable.
Any two Bell pairs between the same two nodes are
indistinguishable for the purposes of an application, provided
they both satisfy its required fidelity threshold. This
observation is likely to be key in enabling a more optimal
allocation of resources in a network, e.g., for the purposes of
provisioning resources to meet application demand. However, the
qubits that make up the pair themselves are not
indistinguishable, and the two nodes operating on a pair must
coordinate to make sure they are operating on qubits that belong
to the same Bell pair.
3. 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 most errors are
effectively eliminated before reaching the application, many
quantum applications only need imperfect entanglement to
function. However, quantum applications will generally have a
threshold for Bell pair fidelity below which they are no longer
able to operate. Different applications will have different
requirements for what fidelity they can work with. It is the
network's responsibility to balance the resource usage with
respect to the applications' requirements. It may be that it is
cheaper for the network to provide lower-fidelity pairs that are
just above the threshold required by the application than it is
to guarantee high-fidelity pairs to all applications regardless
of their requirements.
4. Time is an expensive resource.
Time is not the only resource that is in short supply
(communication qubits and memory are as well), but ultimately it
is the lifetime of quantum memories that imposes some of 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 a Bell
pair to decohere or result in an end-to-end pair below an
application's fidelity threshold. Therefore, managing the idle
time of qubits holding live quantum states should be done
carefully -- ideally by minimising the idle time, but potentially
also by moving the quantum state for temporary storage to a
quantum memory with a longer lifetime.
5. Be flexible with regards to capabilities and limitations.
This goal encompasses two important points:
* First, the architecture should be able to function under the
physical constraints imposed by the current-generation
hardware. Near-future hardware will have low entanglement
generation rates, quantum memories able to hold a handful of
qubits at best, and decoherence rates that will render many
generated pairs unusable.
* Second, the architecture should not make it difficult to run
the network over any hardware that may come along in the
future. The physical capabilities of repeaters will improve,
and redeploying a technology is extremely challenging.
7. A Thought Experiment Inspired by Classical Networks
To conclude, we discuss a plausible quantum network architecture
inspired by MPLS. This is not an architecture proposal but rather a
thought experiment to give the reader an idea of what components are
necessary for a functional quantum network. We use classical MPLS as
a basis, as it is well known and understood in the networking
community.
Creating end-to-end Bell pairs between remote end-points is a
stateful distributed task that requires a lot of a priori
coordination. Therefore, a connection-oriented approach seems the
most natural for quantum networks. In connection-oriented quantum
networks, when two quantum application end-points wish to start
creating end-to-end Bell pairs, they must first create a Quantum
Virtual Circuit (QVC). As an analogy, in MPLS networks, end-points
must establish a Label Switched Path (LSP) before exchanging traffic.
Connection-oriented quantum networks may also support virtual
circuits with multiple end-points for creating multipartite
entanglement. As an analogy, MPLS networks have the concept of
multipoint LSPs for multicast.
When a quantum application creates a QVC, it can indicate Quality of
Service (QoS) parameters such as the required capacity in end-to-end
Bell Pairs Per Second (BPPS) and the required fidelity of the Bell
pairs. As an analogy, in MPLS networks, applications specify the
required bandwidth in Bits Per Second (BPS) and other constraints
when they create a new LSP.
Different applications will have different QoS requirements. For
example, applications such as QKD that don't need to process the
entangled qubits, and only need measure them and store the resulting
outcome, may require a large volume of entanglement but will be
tolerant of delay and jitter for individual pairs. On the other
hand, distributed/cloud quantum computing applications may need fewer
entangled pairs but instead may need all of them to be generated in
one go so that they can all be processed together before any of them
decohere.
Quantum networks need a routing function to compute the optimal path
(i.e., the best sequence of routers and links) for each new QVC. The
routing function may be centralised or distributed. In the latter
case, the quantum network needs a distributed routing protocol. As
an analogy, classical networks use routing protocols such as Open
Shortest Path First (OSPF) and Intermediate System to Intermediate
System (IS-IS). However, note that the definition of "shortest path"
/ "least cost" may be different in a quantum network to account for
its non-classical features, such as fidelity [VanMeter13.2].
Given the very scarce availability of resources in early quantum
networks, a Traffic Engineering (TE) function is likely to be
beneficial. Without TE, QVCs always use the shortest path. In this
case, the quantum network cannot guarantee that each quantum end-
point will get its Bell pairs at the required rate or fidelity. This
is analogous to "best effort" service in classical networks.
With TE, QVCs choose a path that is guaranteed to have the requested
resources (e.g., bandwidth in BPPS) available, taking into account
the capacity of the routers and links and also taking into account
the resources already consumed by other virtual circuits. As an
analogy, both OSPF and IS-IS have TE extensions to keep track of used
and available resources and can use Constrained Shortest Path First
(CSPF) to take resource availability and other constraints into
account when computing the optimal path.
The use of TE implies the use of Call Admission Control (CAC): the
network denies any virtual circuits for which it cannot guarantee the
requested quality of service a priori. Alternatively, the network
preempts lower-priority circuits to make room for a new circuit.
Quantum networks need a signalling function: once the path for a QVC
has been computed, signalling is used to install the "forwarding
rules" into the data plane of each quantum router on the path. The
signalling may be distributed, analogous to the Resource Reservation
Protocol (RSVP) in MPLS. Or, the signalling may be centralised,
similar to OpenFlow.
Quantum networks need an abstraction of the hardware for specifying
the forwarding rules. This allows us to decouple the control plane
(routing and signalling) from the data plane (actual creation of Bell
pairs). The forwarding rules are specified using abstract building
blocks such as "creating local Bell pairs", "swapping Bell pairs", or
"distillation of Bell pairs". As an analogy, classical networks use
abstractions that are based on match conditions (e.g., looking up
header fields in tables) and actions (e.g., modifying fields or
forwarding a packet to a specific interface). The data plane
abstractions in quantum networks will be very different from those in
classical networks due to the fundamental differences in technology
and the stateful nature of quantum networks. In fact, choosing the
right abstractions will be one of the biggest challenges when
designing interoperable quantum network protocols.
In quantum networks, control plane traffic (routing and signalling
messages) is exchanged over a classical channel, whereas data plane
traffic (the actual Bell pair qubits) is exchanged over a separate
quantum channel. This is in contrast to most classical networks,
where control plane traffic and data plane traffic share the same
channel and where a single packet contains both user fields and
header fields. There is, however, a classical analogy to the way
quantum networks work: generalised MPLS (GMPLS) networks use separate
channels for control plane traffic and data plane traffic.
Furthermore, GMPLS networks support data planes where there is no
such thing as data plane headers (e.g., Dense Wavelength Division
Multiplexing (DWDM) or Time-Division Multiplexing (TDM) networks).
8. Security Considerations
Security is listed as an explicit goal for the architecture; this
issue is addressed in Section 6.1. However, as this is an
Informational document, it does not propose any concrete mechanisms
to achieve these goals.
9. IANA Considerations
This document has no IANA actions.
10. Informative References
[Abobeih18]
Abobeih, M.H., Cramer, J., Bakker, M.A., Kalb, N.,
Markham, M., Twitchen, D.J., and T.H. Taminiau, "One-
second coherence for a single electron spin coupled to a
multi-qubit nuclear-spin environment", Nature
communications Vol. 9, Iss. 1, pp. 1-8,
DOI 10.1038/s41467-018-04916-z, June 2018,
.
[Aguado19] Aguado, A., Lopez, V., Lopez, D., Peev, M., Poppe, A.,
Pastor, A., Folgueira, J., and V. Martin, "The Engineering
of Software-Defined Quantum Key Distribution Networks",
IEEE Communications Magazine Vol. 57, Iss. 7, pp. 20-26,
DOI 10.1109/MCOM.2019.1800763, July 2019,
.
[Askarani21]
Askarani, M.F., Chakraborty, K., and G.C. do Amaral,
"Entanglement distribution in multi-platform buffered-
router-assisted frequency-multiplexed automated repeater
chains", New Journal of Physics Vol. 23, Iss. 6, 063078,
DOI 10.1088/1367-2630/ac0a35, June 2021,
.
[Aspect81] Aspect, A., Grangier, P., and G. Roger, "Experimental
Tests of Realistic local Theories via Bell's Theorem",
Physical Review Letters Vol. 47, Iss. 7, pp. 460-463,
DOI 10.1103/PhysRevLett.47.460, August 1981,
.
[Bennett14]
Bennett, C.H. and G. Brassard, "Quantum cryptography:
Public key distribution and coin tossing", Theoretical
Computer Science Vol. 560 (Part 1), pp. 7-11,
DOI 10.1016/j.tcs.2014.05.025, December 2014,
.
[Bennett93]
Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R.,
Peres, A., and W.K. Wootters, "Teleporting an unknown
quantum state via dual classical and Einstein-Podolsky-
Rosen channels", Physical Review Letters Vol. 70, Iss. 13,
pp. 1895-1899, DOI 10.1103/PhysRevLett.70.1895, March
1993, .
[Bennett96]
Bennett, C.H., DiVincenzo, D.P., Smolin, J.A., and W.K.
Wootters, "Mixed-state entanglement and quantum error
correction", Physical Review A Vol. 54, Iss. 5, pp.
3824-3851, DOI 10.1103/PhysRevA.54.3824, November 1996,
.
[Bradley19]
Bradley, C.E., Randall, J., Abobeih, M.H., Berrevoets,
R.C., Degen, M.J., Bakker, M.A., Markham, M., Twitchen,
D.J., and T.H. Taminiau, "A Ten-Qubit Solid-State Spin
Register with Quantum Memory up to One Minute", Physical
Review X Vol. 9, Iss. 3, 031045,
DOI 10.1103/PhysRevX.9.031045, September 2019,
.
[Briegel98]
Briegel, H.-J., Dür, W., Cirac, J.I., and P. Zoller,
"Quantum Repeaters: The Role of Imperfect Local Operations
in Quantum Communication", Physical Review Letters Vol.
81, Iss. 26, pp. 5932-5935,
DOI 10.1103/PhysRevLett.81.5932, December 1998,
.
[Broadbent10]
Broadbent, A., Fitzsimons, J., and E. Kashefi,
"Measurement-Based and Universal Blind Quantum
Computation", Springer-Verlag 978-3-642-13678-8,
DOI 10.1007/978-3-642-13678-8_2, June 2010,
.
[Cacciapuoti19]
Cacciapuoti, A.S., Caleffi, M., Van Meter, R., and L.
Hanzo, "When Entanglement Meets Classical Communications:
Quantum Teleportation for the Quantum Internet", IEEE
Transactions on Communications Vol. 68, Iss. 6, pp.
3808-3833, DOI 10.1109/TCOMM.2020.2978071, June 2020,
.
[Cirac99] Cirac, J.I., Ekert, A.K., Huelga, S.F., and C.
Macchiavello, "Distributed quantum computation over noisy
channels", Physical Review A Vol. 59, Iss. 6, 4249,
DOI 10.1103/PhysRevA.59.4249, June 1999,
.
[Clark88] Clark, D., "The design philosophy of the DARPA internet
protocols", SIGCOMM '88: Symposium proceedings on
Communications architectures and protocols, pp. 106-114,
DOI 10.1145/52324.52336, August 1988,
.
[Crepeau02]
Crépeau, C., Gottesman, D., and A. Smith, "Secure multi-
party quantum computation", STOC '02: Proceedings of the
thiry-fourth [sic] annual ACM symposium on Theory of
computing, pp. 643-652, DOI 10.1145/509907.510000, May
2002, .
[Dahlberg19]
Dahlberg, A., Skrzypczyk, M., Coopmans, T., Wubben, L.,
Rozpędek, F., Pompili, M., Stolk, A., Pawełczak, P.,
Knegjens, R., de Oliveira Filho, J., Hanson, R., and S.
Wehner, "A link layer protocol for quantum networks",
SIGCOMM '19 Proceedings of the ACM Special Interest Group
on Data Communication, pp. 159-173,
DOI 10.1145/3341302.3342070, August 2019,
.
[Devitt13] Devitt, S.J., Munro, W.J., and K. Nemoto, "Quantum error
correction for beginners", Reports on Progress in Physics
Vol. 76, Iss. 7, 076001,
DOI 10.1088/0034-4885/76/7/076001, June 2013,
.
[DistCNOT] "Distributed CNOT", Quantum Network Explorer by QuTech,
2023, .
[Dur07] Dür, W. and H.J. Briegel, "Entanglement purification and
quantum error correction", Reports on Progress in Physics
Vol. 70, Iss. 8, pp. 1381-1424,
DOI 10.1088/0034-4885/70/8/R03, July 2007,
.
[Ekert91] Ekert, A.K., "Quantum cryptography based on Bell's
theorem", Physical Review Letters Vol. 67, Iss. 6, pp.
661-663, DOI 10.1103/PhysRevLett.67.661, August 1991,
.
[Elkouss11]
Elkouss, D., Martinez-Mateo, J., and V. Martin,
"Information Reconciliation for Quantum Key Distribution",
Quantum Information and Computation Vol. 11, No. 3 and 4,
pp. 0226-0238, DOI 10.48550/arXiv.1007.1616, March 2011,
.
[Elliott03]
Elliott, C., Pearson, D., and G. Troxel, "Quantum
cryptography in practice", SIGCOMM 2003: Proceedings of
the 2003 conference on Applications, technologies,
architectures, and protocols for computer communications,
pp. 227-238, DOI 10.1145/863955.863982, August 2003,
.
[Fitzsimons17]
Fitzsimons, J.F. and E. Kashefi, "Unconditionally
verifiable blind quantum computation", Physical Review A
Vol. 96, Iss. 1, 012303, DOI 10.1103/PhysRevA.96.012303,
July 2017, .
[Fowler10] Fowler, A.G., Wang, D.S., Hill, C.D., Ladd, T.D., Van
Meter, R., and L.C.L. Hollenberg, "Surface Code Quantum
Communication", Physical Review Letters Vol. 104, Iss. 18,
180503, DOI 10.1103/PhysRevLett.104.180503, May 2010,
.
[Giovannetti04]
Giovannetti, V., Lloyd, S., and L. Maccone, "Quantum-
Enhanced Measurements: Beating the Standard Quantum
Limit", Science Vol. 306, Iss. 5700, pp. 1330-1336,
DOI 10.1126/science.1104149, November 2004,
.
[Gottesman12]
Gottesman, D., Jennewein, T., and S. Croke, "Longer-
Baseline Telescopes Using Quantum Repeaters", Physical
Review Letters Vol. 109, Iss. 7, 070503,
DOI 10.1103/PhysRevLett.109.070503, August 2012,
.
[Hensen15] Hensen, B., Bernien, H., Dréau, A.E., Reiserer, A., Kalb,
N., Blok, M.S., Ruitenberg, J., Vermeulen, R.F.L.,
Schouten, R.N., Abellán, C., Amaya, W., Pruneri, V.,
Mitchell, M.W., Markham, M., Twitchen, D.J., Elkouss, D.,
Wehner, S., Taminiau, T.H., and R. Hanson, "Loophole-free
Bell inequality violation using electron spins separated
by 1.3 kilometres", Nature Vol. 526, pp. 682-686,
DOI 10.1038/nature15759, October 2015,
.
[Jiang09] Jiang, L., Taylor, J.M., Nemoto, K., Munro, W.J., Van
Meter, R., and M.D. Lukin, "Quantum repeater with
encoding", Physical Review A Vol. 79, Iss. 3, 032325,
DOI 10.1103/PhysRevA.79.032325, March 2009,
.
[Joshi20] Joshi, S.K., Aktas, D., Wengerowsky, S., Lončarić, M.,
Neumann, S.P., Liu, B., Scheidl, T., Currás-Lorenzo, G.,
Samec, Z., Kling, L., Qiu, A., Razavi, M., Stipčević, M.,
Rarity, J.G., and R. Ursin, "A trusted node-free eight-
user metropolitan quantum communication network", Science
Advances Vol. 6, no. 36, eaba0959,
DOI 10.1126/sciadv.aba0959, September 2020,
.
[Kimble08] Kimble, H.J., "The quantum internet", Nature Vol. 453,
Iss. 7198, pp. 1023-1030, DOI 10.1038/nature07127, June
2008, .
[Komar14] Kómár, P., Kessler, E.M., Bishof, M., Jiang, L., Sørensen,
A.S., Ye, J., and M.D. Lukin, "A quantum network of
clocks", Nature Physics Vol. 10, Iss. 8, pp. 582-587,
DOI 10.1038/nphys3000, June 2014,
.
[Meignant19]
Meignant, C., Markham, D., and F. Grosshans, "Distributing
graph states over arbitrary quantum networks", Physical
Review A Vol. 100, Iss. 5, 052333,
DOI 10.1103/PhysRevA.100.052333, November 2019,
.
[Moehring07]
Moehring, D.L., Maunz, P., Olmschenk, S., Younge, K.C.,
Matsukevich, D.N., Duan, L.-M., and C. Monroe,
"Entanglement of single-atom quantum bits at a distance",
Nature Vol. 449, Iss. 7158, pp. 68-71,
DOI 10.1038/nature06118, September 2007,
.
[Mural16] Muralidharan, S., Li, L., Kim, J., Lütkenhaus, N., Lukin,
M.D., and L. Jiang, "Optimal architectures for long
distance quantum communication", Scientific Reports Vol.
6, pp. 1-10, DOI 10.1038/srep20463, February 2016,
.
[Murta20] Murta, G., Grasselli, F., Kampermann, H., and D. Bruß,
"Quantum Conference Key Agreement: A Review", Advanced
Quantum Technologies Vol. 3, Iss. 11, 2000025,
DOI 10.1002/qute.202000025, September 2020,
.
[Nagayama16]
Nagayama, S., Choi, B.-S., Devitt, S., Suzuki, S., and R.
Van Meter, "Interoperability in encoded quantum repeater
networks", Physical Review A Vol. 93, Iss. 4, 042338,
DOI 10.1103/PhysRevA.93.042338, April 2016,
.
[Nagayama21]
Nagayama, S., "Towards End-to-End Error Management for a
Quantum Internet", arXiv 2112.07185,
DOI 10.48550/arXiv.2112.07185, December 2021,
.
[NielsenChuang]
Nielsen, M.A. and I.L. Chuang, "Quantum Computation and
Quantum Information", Cambridge University Press, 2010,
.
[Park70] Park, J.L., "The concept of transition in quantum
mechanics", Foundations of Physics Vol. 1, Iss. 1, pp.
23-33, DOI 10.1007/BF00708652, March 1970,
.
[Peev09] Peev, M., Pacher, C., Alléaume, R., Barreiro, C., Bouda,
J., Boxleitner, W., Debuisschert, T., Diamanti, E.,
Dianati, M., Dynes, J.F., Fasel, S., Fossier, S., Fürst,
M., Gautier, J.-D., Gay, O., Gisin, N., Grangier, P.,
Happe, A., Hasani, Y., Hentschel, M., Hübel, H., Humer,
G., Länger, T., Legré, M., Lieger, R., Lodewyck, J.,
Lorünser, T., Lütkenhaus, N., Marhold, A., Matyus, T.,
Maurhart, O., Monat, L., Nauerth, S., Page, J.-B., Poppe,
A., Querasser, E., Ribordy, G., Robyr, S., Salvail, L.,
Sharpe, A.W., Shields, A.J., Stucki, D., Suda, M., Tamas,
C., Themel, T., Thew, R.T., Thoma, Y., Treiber, A.,
Trinkler, P., Tualle-Brouri, R., Vannel, F., Walenta, N.,
Weier, H., Weinfurter, H., Wimberger, I., Yuan, Z.L.,
Zbinden, H., and A. Zeilinger, "The SECOQC quantum key
distribution network in Vienna", New Journal of Physics
Vol. 11, Iss. 7, 075001,
DOI 10.1088/1367-2630/11/7/075001, July 2009,
.
[Pompili21.1]
Pompili, M., Hermans, S.L.N., Baier, S., Beukers, H.K.C.,
Humphreys, P.C., Schouten, R.N., Vermeulen, R.F.L.,
Tiggelman, M.J., dos Santos Martins, L., Dirkse, B.,
Wehner, S., and R. Hanson, "Realization of a multinode
quantum network of remote solid-state qubits", Science
Vol. 372, No. 6539, pp. 259-264,
DOI 10.1126/science.abg1919, April 2021,
.
[Pompili21.2]
Pompili, M., Delle Donne, C., te Raa, I., van der Vecht,
B., Skrzypczyk, M., Ferreira, G., de Kluijver, L., Stolk,
A.J., Hermans, S.L.N., Pawełczak, P., Kozlowski, W.,
Hanson, R., and S. Wehner, "Experimental demonstration of
entanglement delivery using a quantum network stack", npj
Quantum Information Vol. 8, 121, DOI 10.4121/16912522,
October 2022,
.
[QI-Scenarios]
Wang, C., Rahman, A., Li, R., Aelmans, M., and K.
Chakraborty, "Application Scenarios for the Quantum
Internet", Work in Progress, Internet-Draft, draft-irtf-
qirg-quantum-internet-use-cases-15, 10 March 2023,
.
[Qin17] Qin, H. and Y. Dai, "Dynamic quantum secret sharing by
using d-dimensional GHZ state", Quantum information
processing Vol. 16, Iss. 3, 64,
DOI 10.1007/s11128-017-1525-y, January 2017,
.
[QKD] "Quantum Key Distribution", Quantum Network Explorer by
QuTech, 2023,
.
[RFC1958] Carpenter, B., Ed., "Architectural Principles of the
Internet", RFC 1958, DOI 10.17487/RFC1958, June 1996,
.
[Sangouard11]
Sangouard, N., Simon, C., de Riedmatten, H., and N. Gisin,
"Quantum repeaters based on atomic ensembles and linear
optics", Reviews of Modern Physics Vol. 83, Iss. 1, pp.
33-80, DOI 10.1103/RevModPhys.83.33, March 2011,
.
[Satoh17] Satoh, T., Nagayama, S., Oka, T., and R. Van Meter, "The
network impact of hijacking a quantum repeater", Quantum
Science and Technology Vol. 3, Iss. 3, 034008,
DOI 10.1088/2058-9565/aac11f, May 2018,
.
[Satoh20] Satoh, T., Nagayama, S., Suzuki, S., Matsuo, T., Hajdušek,
M., and R. Van Meter, "Attacking the Quantum Internet",
IEEE Transactions on Quantum Engineering, vol. 2, pp.
1-17, DOI 10.1109/TQE.2021.3094983, September 2021,
.
[SutorBook]
Sutor, R.S., "Dancing with Qubits", Packt Publishing,
November 2019, .
[Tang19] Tang, B.-Y., Liu, B., Zhai, Y.-P., Wu, C.-Q., and W.-R.
Yu, "High-speed and Large-scale Privacy Amplification
Scheme for Quantum Key Distribution", Scientific Reports
Vol. 9, DOI 10.1038/s41598-019-50290-1, October 2019,
.
[Teleportation]
"State teleportation", Quantum Network Explorer by QuTech,
2023, .
[Terhal04] Terhal, B.M., "Is entanglement monogamous?", IBM Journal
of Research and Development Vol. 48, Iss. 1, pp. 71-78,
DOI 10.1147/rd.481.0071, January 2004,
.
[VanMeter13.1]
Van Meter, R. and J. Touch, "Designing quantum repeater
networks", IEEE Communications Magazine Vol. 51, Iss. 8,
pp. 64-71, DOI 10.1109/MCOM.2013.6576340, August 2013,
.
[VanMeter13.2]
Van Meter, R., Satoh, T., Ladd, T.D., Munro, W.J., and K.
Nemoto, "Path selection for quantum repeater networks",
Networking Science Vol. 3, Iss. 1-4, pp. 82-95,
DOI 10.1007/s13119-013-0026-2, December 2013,
.
[VanMeterBook]
Van Meter, R., "Quantum Networking", ISTE Ltd/John Wiley
and Sons. Inc., Print ISBN 978-1-84821-537-5,
DOI 10.1002/9781118648919, April 2014,
.
[Wang21] Wang, L.-J., Zhang, K.-Y., Wang, J.-Y., Cheng, J., Yang,
Y.-H., Tang, S.-B., Yan, D., Tang, Y.-L., Liu, Z., Yu, Y.,
Zhang, Q., and J.-W. Pan, "Experimental authentication of
quantum key distribution with post-quantum cryptography",
npj Quantum Information Vol. 7, pp. 1-7,
DOI 10.1038/s41534-021-00400-7, May 2021,
.
[Wehner18] Wehner, S., Elkouss, D., and R. Hanson, "Quantum internet:
A vision for the road ahead", Science Vol. 362, Iss. 6412,
DOI 10.1126/science.aam9288, October 2018,
.
[Wei22] Wei, S.-H., Jing, B., Zhang, X.-Y., Liao, J.-Y., Yuan, C.-
Z., Fan, B.-Y., Lyu, C., Zhou, D.-L., Wang, Y., Deng, G.-
W., Song, H.-Z., Oblak, D., Guo, G.-C., and Q. Zhou,
"Towards Real-World Quantum Networks: A Review", Laser and
Photonics Reviews Vol. 16, 2100219,
DOI 10.1002/lpor.202100219, January 2022,
.
[Wootters82]
Wootters, W.K. and W.H. Zurek, "A single quantum cannot be
cloned", Nature Vol. 299, Iss. 5886, pp. 802-803,
DOI 10.1038/299802a0, October 1982,
.
[ZOO] "The Quantum Protocol Zoo", November 2019,
.
Acknowledgements
The authors want to thank Carlo Delle Donne, Matthew Skrzypczyk, Axel
Dahlberg, Mathias van den Bossche, Patrick Gelard, Chonggang Wang,
Scott Fluhrer, Joey Salazar, Joseph Touch, and the rest of the QIRG
community as a whole for their very useful reviews and comments on
this document.
WK and SW acknowledge funding received from the EU Flagship on
Quantum Technologies, Quantum Internet Alliance (No. 820445).
rdv acknowledges support by the Air Force Office of Scientific
Research under award number FA2386-19-1-4038.
Authors' Addresses
Wojciech Kozlowski
QuTech
Building 22
Lorentzweg 1
2628 CJ Delft
Netherlands
Email: w.kozlowski@tudelft.nl
Stephanie Wehner
QuTech
Building 22
Lorentzweg 1
2628 CJ Delft
Netherlands
Email: s.d.c.wehner@tudelft.nl
Rodney Van Meter
Keio University
5322 Endo, Fujisawa, Kanagawa
252-0882
Japan
Email: rdv@sfc.wide.ad.jp
Bruno Rijsman
Individual
Email: brunorijsman@gmail.com
Angela Sara Cacciapuoti
University of Naples Federico II
Department of Electrical Engineering and Information Technologies
Claudio 21
80125 Naples
Italy
Email: angelasara.cacciapuoti@unina.it
Marcello Caleffi
University of Naples Federico II
Department of Electrical Engineering and Information Technologies
Claudio 21
80125 Naples
Italy
Email: marcello.caleffi@unina.it
Shota Nagayama
Mercari, Inc.
Roppongi Hills Mori Tower 18F
6-10-1 Roppongi, Minato-ku, Tokyo
106-6118
Japan
Email: shota.nagayama@mercari.com