Towards Large-Scale Quantum Networks

Abstract

The vision of a quantum internet is to fundamentally enhance Internet technology by enabling quantum communication between any two points on Earth. While the first realisations of small scale quantum networks are expected in the near future, scaling such networks presents immense challenges to physics, computer science and engineering. Here, we provide a gentle introduction to quantum networking targeted at computer scientists, and survey the state of the art. We proceed to discuss key challenges for computer science in order to make such networks a reality.

Full text

Towards Large-Scale antum Networks
Wojciech Kozlowski
w.kozlowski@tudelft.nl
QuTech, Delft University of Technology
Delft, Netherlands
Stephanie Wehner
s.d.c.wehner@tudelft.nl
QuTech, Delft University of Technology
Delft, Netherlands
ABSTRACT
The vision of a quantum internet is to fundamentally enhance
Internet technology by enabling quantum communication between
any two points on Earth. While the rst realisations of small scale
quantum networks are expected in the near future, scaling such
networks presents immense challenges to physics, computer science
and engineering. Here, we provide a gentle introduction to quantum
networking targeted at computer scientists, and survey the state of
the art. We proceed to discuss key challenges for computer science
in order to make such networks a reality.
CCS CONCEPTS
•Networks →Network architectures
;
Network protocols
;
Net-
work components
;
•Computer systems organization →Quan-
tum computing.
KEYWORDS
networks, quantum networks, quantum internet, network protocols,
quantum communications, quantum computing
ACM Reference Format:
Wojciech Kozlowski and Stephanie Wehner. 2019. Towards Large-Scale
Quantum Networks. In The Sixth Annual ACM International Conference
on Nanoscale Computing and Communication (NANOCOM ’19), September
25–27, 2019, Dublin, Ireland. ACM, New York, NY, USA, 7 pages. https:
//doi.org/10.1145/3345312.3345497
1 INTRODUCTION
The objective of quantum networks is to fundamentally enhance
communication technology by allowing the transmission and ma-
nipulation of quantum bits (qubits) between remote locations. Such
networks will be embedded within classical networks as shown
in Fig. 1 and applications will have access to both quantum and
classical channels. Quantum networks will be used to execute pro-
tocols that have no classical counterpart or are more ecient than
what is possible classically. The range of possible quantum appli-
cations will depend on the development stage of the underlying
hardware hardware [
67
]. This new networking paradigm has al-
ready opened up a range of new applications, which are provably
impossible to realise using classical communication over the inter-
net that we have today. Quantum key distribution (QKD) [
2
,
19
] to
Permission to make digital or hard copies of all or part of this work for personal or
classroom use is granted without fee provided that copies are not made or distributed
for prot or commercial advantage and that copies bear this notice and the full citation
on the rst page. Copyrights for components of this work owned by others than ACM
must be honored. Abstracting with credit is permitted. To copy otherwise, or republish,
to post on servers or to redistribute to lists, requires prior specic permission and/or a
fee. Request permissions from permissions@acm.org.
NANOCOM ’19, September 25–27, 2019, Dublin, Ireland
©2019 Association for Computing Machinery.
ACM ISBN 978-1-4503-6897-1/19/09.. .$15.00
https://doi.org/10.1145/3345312.3345497
ensure secure communication is the most famous example as it is
also the only application that is ready for commercialisation and
is undergoing standardisation. Whilst QKD will be the main focus
for most near-term quantum networks, many other applications
have already been put forward, with many more to be expected
when such networks become widespread such as secure quantum
computing in the cloud [
10
,
21
], clock synchronisation [
34
], and
sensor networks [22, 23].
Figure 1: Quantum networks will be embedded within clas-
sical networks and use existing infrastructure to send and
receive control messages. This can be achieved by adding
a quantum data plane to existing networks. Note that the
quantum and classical links do not have to coincide.
Using features of quantum mechanics as the underlying physical
mechanism for communication opens up many new possibilities,
but also introduces considerable new design challenges. Some of
these design challenges are due to fundamental dierences between
quantum and classical information, while others arise from techno-
logical limitations in engineering large-scale quantum systems. The
rst fundamental dierence that quantum communication brings
with it is the no-cloning theorem [
43
]. That is, arbitrary quantum
data cannot be copied without destroying the original version. This
means that it is impossible to use the same solutions that worked
for classical networks which rely heavily on the ability to read and
copy data for the purposes of retransmission and signal amplica-
tion. These limitations make transmitting qubits over long distances
particularly challenging. The second fundamental dierence arises
due to a phenomenon called quantum entanglement. Entanglement
is a special state of two or more qubits, that can in principle persist
even if they are separated by arbitrary geographical distances and
arXiv:1909.08396v1 [cs.NI] 6 Sep 2019

NANOCOM ’19, September 25–27, 2019, Dublin, Ireland Wojciech Kozlowski and Stephanie Wehner
it is the key ingredient that enables long distance quantum commu-
nication. This property exists at the physical level and it requires
that the location and state of its constituent qubits be known at all
times. This is in contrast to classical communication, where signals
at the physical layer typically proceed from the sender to the re-
ceiver and no state or notion of a connection exists. This introduces
new demands for the control of such networks, as quantum data is
inherently delocalised across multiple devices.
Design considerations that come from technological and not just
fundamental limitations form an integral part of quantum network
development and a key issue when considering realistic deploy-
ments. The technological challenges are immense, and include —
for example — storing qubits for a long time or manipulating a large
number of qubits simultaneously.
The remainder of this paper is structured as follows: Section 2
briey surveys the current state of the art of quantum networked
technologies and in Section 3 we give a basic introduction to the
quantum physics of such networks. In Sections 4 and 5 we discuss
the elements of a quantum network and a possible network stack
respectively. Future research challenges are presented in Section 6
and the paper is concluded in 7.
2 STATE OF THE ART
At present, no large-scale quantum networks exist. At short dis-
tances (~100 km in telecom bre), devices that perform QKD are
commercially available [
16
,
20
,
22
,
32
]. Early-stage demonstrations
also achieve longer distances in the lab using coiled bre [
5
,
29
,
39
,
57
,
66
,
72
], or through free space communication [
54
,
61
]. QKD
devices have been deployed in a variety of eld tests and short-
distance networks [47, 52, 56, 65].
While no long-distance quantum networks exist, short distance
segments have been chained together classically to form so-called
trusted repeater or trusted node networks [
50
,
53
]. Such networks
do not allow the end to end transmission of qubits, or the genera-
tion of entanglement and hence do not oer end-to-end security.
They only enable secure communication between two end-points,
provided that all the intermediate nodes are trusted. Such links of
trusted nodes have been realised [
14
,
52
], but require a high level
of physical security to protect the trusted nodes. Such devices only
produce short-lived (entanglement is not stored), short-distance
entanglement and lack any of the features needed to bridge longer
distances.
Long-range quantum communication, as well as the realisations
of networks with functionalities more advanced than QKD, are
presently still in their infancy. Entanglement between distant sites
(~1200 km) has been produced using a satellite [
68
]. However, data
rates (~1 hz for 275 s per day) are still too low to produce a secret
key, and the entanglement is short-lived. The present record for
producing heralded entanglement between distant sites is 1.3 km
in a solid state quantum device (nitrogen-vacancy (NV) centres in
diamond) [
28
]. Longer distances have been observed for nodes in
the same lab [
70
]. Demonstrations of more complex applications
such as blind quantum computing [
1
] and quantum sensing [
24
]
have also been realised in laboratory conditions.
Going forward, we would like to improve early-stage quantum
communication in three directions. First, we would like to enable
untrusted long-distance communication. Second, we would also like
to enable the execution of more complex quantum network applica-
tions in order to take full advantage of our ability to transmit qubits.
And nally, we would like to improve accessibility by allowing early
stage access to such technology. The rst realisation of such a net-
work, a four-node demonstration in the Netherlands, is scheduled
to be operational within the next 5–6 years. Much essential work
is being done to build quantum hardware to make this possible,
which is covered at length in the physics literature [41, 51, 67].
3 QUBITS AND ENTANGLEMENT
This subsection will briey introduce the basic concepts of quantum
computing and networking: qubits, quantum gates, and entangle-
ment. For additional information see e.g. [43].
3.1 Qubits
The dierences between quantum computation and classical com-
putation begin at the bit-level. A classical computer operates on
the binary alphabet
{
0
,
1
}
. Mathematically, a quantum bit, a qubit,
exists over the same binary space, but unlike the classical bit, it can
exist in a so-called superposition of the two possibilities:
|Ψ⟩=α|0⟩+β|1⟩(1)
where
|X⟩
denotes a quantum state, here the binary 0and 1, and
the coecients
α
and
β
are complex numbers called probability
amplitudes satisfying |α|2+|β|2=1.
Upon measurement
1
, the qubit loses its superposition and irre-
versibly collapses into one of the two basis states, either
|
0
⟩
or
|
1
⟩
,
and yields the corresponding value, 0or 1, as the measurement
readout. The outcome of the measurement is not deterministic, and
the probability of measuring 0and collapsing the state to
|
0
⟩
is
|α|2
and similarly the probability of measuring 1and collapsing the
state to
|
1
⟩
is
|β|2
. This randomness is not due to our ignorance of
the underlying mechanisms, but rather it is a fundamental feature
of a quantum mechanical system.
Many possible realisations of qubits exists. Key to all these repre-
sentations, is to nd a realisation of the classical states
|
0
⟩
and
|
1
⟩
,
together with a procedure to create arbitrary superpositions
|Ψ⟩
thereof. For quantum memories, and quantum computing devices,
|
0
⟩
and
|
1
⟩
typically correspond to states of two dierent energies
in either a natural “atomic system” (e.g. ion traps [
27
], NV centres
in diamond [
60
], neutral atoms [
8
] or atomic ensembles [
51
]), or
articially designed nano-scale systems (e.g. superconducting quan-
tum processors [
13
]). For transmission, usually optically, qubits can
be represented in a variety of ways: the two states
|
0
⟩
and
|
1
⟩
can be
encoded in the presence or absence of a photon [
11
,
31
], a time-bin
encoding of early and late arrival [
7
], or the horizontal and vertical
polarisation of photons [2, 38].
3.2 Multiple Qubits
We can express the state of an n-qubit quantum state as
|Ψ⟩=Õ
x∈{0,1}n
αx|x⟩,(2)
1In the standard basis, given by {|0⟩,|1⟩}

Towards Large-Scale antum Networks NANOCOM ’19, September 25–27, 2019, Dublin, Ireland
where
Íx|αx|2=
1. We remark that this means that since there are
2
n
possible strings
x∈ {0,1}n
, we need an exponential number of
parameters
αx∈C
in order to describe the denite state
|Ψ⟩
. This
is in sharp contrast to classical computing, where only
n
parameters
are needed (namely a specic string x).
As an example, if we have two qubits
A
and
B
, and the rst qubit
is in a state
|
0
⟩A
and the second in a state
|
1
⟩B
, then the overall state
of the two qubits can be expressed as
|
01
⟩=|
0
⟩A|
1
⟩B
. However,
there exists multi-qubit states
|Ψ⟩
which cannot be written as such
a combination of single qubit states. That is, the two qubits can non
longer be described independently of each other. The states of the
two individual qubits are now correlated beyond what is possible to
achieve classically. Such states are called entangled. For two-qubits
the maximally entangled state can (up to local quantum gates) be
written as
|Φ⟩=1
√2(|0⟩A|0⟩B+|1⟩A|1⟩B).(3)
Such states have an interesting property that for any measurement
on
A
that probabilistically yields outcome
x
, there always exists a
measurement on
B
that yields exactly the same outcome
x
. Very
intuitively, such states can hence be understood as the quantum
analogue of maximal correlation in the classical domain, only such
correlations persist for any measurement. Entanglement enables
much stronger than classical correlations, also for more complex
scenarios [
62
]. Interestingly, entanglement cannot be shared, which
is also known as the monogamy of entanglement [59].
An entangled state is created from initially unentangled qubits,
say
|
0
⟩A|
0
⟩B
. A common scheme to locally create an entangled state
is to start by applying the so-called Hadamard operation on
A
to
produce
(|
0
⟩A+|
1
⟩A)|
0
⟩B/√2
. Subsequently a controlled NOT oper-
ation (CNOT) is performed which has the eect
CNOT|x⟩A|y⟩B=
|x⟩A|y+xmod 2⟩:
CNOT 1
√2(|0⟩A|0⟩B+|1⟩A|0⟩B)=1
√2(|0⟩A|0⟩B+|1⟩A|1⟩B).
(4)
The physical implementation depends on the underlying hardware
platform. For NV centres in diamond this operation can be imple-
mented using a combination of a microwave and optical pulses [
28
].
3.3 Teleportation
Qubits may be transmitted directly, or via quantum teleportation [
3
]
using entanglement. To teleport one data qubit
|Ψ⟩
, we require one
entangled pair
|Φ⟩
to be established between the sender and receiver
ahead of time. The sender performs a measurement of the data qubit
|Ψ⟩
and their qubit
A
of
|Φ⟩
(see Fig. 2), resulting in two classical
bits
y∈ {0,1}2
as the measurement outcome. The sender transmits
y
to the receiver, who applies a correction depending on
y
on their
qubit in order to recover
|Ψ⟩
. From the perspective of control of
such a network, we remark that this requires that the sender has
correctly identied that qubit
A
belongs to the entangled state
|Φ⟩
shared with the receiver, and that the entanglement is consumed
by this process. Deterministic teleportation has been realised, using
for example two network nodes based on NV in diamond [48].
Teleportation is crucial for quantum networking. The no-cloning
theorem means that retransmitting the data qubit if sending fails is
not an option. However,
|Φ⟩
is a known generic state that does not
carry any data and can be repeatedly recreated until it has been
successfully distributed to the sender and receiver. At this point
the sender simply teleports the sensitive data qubit to the receiver
without putting it through the network risking its loss.
Figure 2: Entangled Bell pairs enable long-distance quantum
communication. (a) An unknown data qubit state can be tele-
ported over long distances by consuming a Bell pair that has
one qubit at the source and the other qubit at the destination.
(b) Two shorter Bell pairs can be combined into a longer Bell
pair with an entanglement swap operation.
3.4 Entanglement Swapping
Teleportation also provides a mechanism to extend short-distance
entanglement to larger distances [
9
,
18
,
41
]. Consider node
A
which
has generated entanglement with node
B
. Similarly,
B
has produced
entanglement with
C
. We can now generate entanglement between
A
and
C
using the help of
B
:
B
teleports the qubit entangled with
node
A
to
C
, using the entanglement he shares with
C
. This process
is also known as entanglement swapping [9, 73] (see Fig. 2).
Unfortunately, neither the entanglement generation nor the
swapping operations are noiseless. Therefore, with each link and
each swap the quality of the entanglement, called delity, degrades.
However, it is possible to create higher delity entangled pairs from
two or more lower quality pair states through a process called dis-
tillation using the Purify-and-Swap algorithm [
9
]. Therefore, once
the quality loss over a given distance become prohibitive, additional
redundancy may be used to restore the state delity.
4 ELEMENTS OF A QUANTUM NETWORK
Let us provide a high-level overview of the elements of a quantum
network [
67
]. For additional overview of design considerations for
quantum networks we also refer to Refs. [15, 62, 64].
End Nodes: Just like in classical networks we need devices at
the edge of the network on which applications are run. In the sim-
plest case, these are photonic devices consisting of linear optical
elements, photon sources and detectors. These do not have a quan-
tum memory to store qubits, and can also only perform a limited
set of quantum operations deterministically. However, these are
sucient to perform all protocols in the prepare and measure stage
of quantum network [
67
] at short distances (presently ~100 km over
deployed telecom bre), such as QKD.
However, they may also be processing nodes with an optical in-
terface which are capable of storing qubits, as well as performing
universal quantum computation. Examples include NV centres in
diamond [
4
,
28
,
58
], ion traps [
40
], and neutral atoms [
49
]. Such sys-
tems can also be used to run application protocols in the quantum
memory network stage and eventually above [67].

NANOCOM ’19, September 25–27, 2019, Dublin, Ireland Wojciech Kozlowski and Stephanie Wehner
Quantum repeaters: The objective of quantum repeaters is to
transmit qubits over long-distances. Any system that is a quan-
tum processing node, can also be used as a repeater platform. In
addition, there exist specic hardware platforms tailored to the
task of a quantum repeater. This includes multiplexed quantum
repeaters [
51
] which promise to generate entanglement quickly by
temporal and spatial multiplexing. These repeater platforms work —
in a possible combination with entanglement distillation steps — by
the entanglement swapping principle outlined in Fig. 2. Theoretical
proposals for employing forward error correction also exist [
42
],
but they are not possible to realise in the near-term.
The current world record for producing such heralded (i.e. con-
rmed) entanglement is 1.3 km which has been achieved using NV
centres in diamond [
28
], see Fig. 3. This platform is a few (about
10 [
6
]) qubit quantum computer with an optical interface capable of
executing arbitrary gates and measurements. It has been recently
demonstrated that NV centres are capable of memory lifetimes ap-
proaching one minute [
6
] in nodes not yet interfaced to the network.
Other platforms exist that are similar on the conceptual level with
similar capabilities such as ion traps [
33
] and neutral atoms [
49
]
(see Table 1 for current parameter trade-os).
Figure 3: Example of a physical implementation producing
entanglement between two quantum processors (NV in dia-
mond). (a) The qubits of the Bell pair are stored in NV cen-
tres in diamond on (b) custom chips. (c) Entanglement is gen-
erated between the two processors using probabilistic entan-
glement swapping: entanglement is produced between each
processor and a traveling qubit (photon) sent to the mid-
point. The mid-point performs entanglement swapping, and
sends a conrmation (heralding) signal back to the nodes
whether entanglement generation was a success.
Communication lines: Qubits can be sent using photons through
bre, or free space communication [
70
]. Standard telecom bre
can be used for this purpose, potentially following an appropriate
wavelength conversion to the telecom band [17, 71].
Classical Control Messages. A crucial component of quantum
communication is also the ability to send classical data. The control
Table 1: Quantum Link Eciency (QLE) is given by the ra-
tio of the entangling rate to the decoherence rate, capturing
how fast entanglement can be produced in relation to how
fast it is lost. A QLE ≥
1
is required to extend entanglement
over long distances.
Platform QLE
NV Centres 8 [31]
Trapped Ions 5 [30]
Neutral Atoms 2 (projected) [35, 44]
of quantum devices requires quite a number of classical control sig-
nals to be exchange, teleportation being just one example. In order
to develop functional quantum protocols we will need a way to
transmit control information between the quantum repeaters. This
means that it is expected that quantum networks will be deployed
alongside classical networks with a quantum data plane coexisting
with the classical one as shown in Fig. 1.
5 A QUANTUM NETWORK STACK
One may wonder whether one can design quantum network pro-
tocols without detailed knowledge of the underlying hardware
system. Here, we briey summarise the approach of Ref. [
15
], be-
cause it is dened in terms of service layers rather than protocol
layers (see Fig. 4) which gives it a structure that is similar to the
classical TCP/IP stack. It also gives a concrete link layer protocol
that abstracts away from the underlying hardware system, turning
entanglement generation into a well-dened service.
Figure 4: Functional allocation in a quantum network stack.
The structure mirrors and is inspired by the classical TCP/IP
network stack.
Physical. This layer corresponds to the actual quantum hardware
devices and physical connections. The physical layer keeps no state
related to entanglement production, produced entanglement proba-
bilistically, and has no decision making capabilities. The hardware
is solely responsible for tasks such as time synchronisation, photon
emission, laser phase stabilisation, and so on, that are required to
actually produce entangled Bell pairs.
Link. The task of the link-layer is to utilise the physical layer’s
ability to produce entanglement between neighbouring nodes reli-
ably. It also integrates the quantum and classical data planes provid-
ing sucient information for higher level protocols and network
management. A concrete link layer protocol can be found in [15].

Towards Large-Scale antum Networks NANOCOM ’19, September 25–27, 2019, Dublin, Ireland
Network. Similar to a network layer in classical networking, the
task of the network layer is to enable the generation of entangle-
ment between network nodes which are not directly connected. A
protocol to achieve this would utilise the link layer to produce en-
tanglement between neighbouring nodes followed by entanglement
swaps to create long distance links.
Transport. One can imagine, that a transport layer could provide
the additional service of transmitting qubits to the application layer.
This could be realised by, for example, pre-generating entangled
pairs of qubits using the network layer, followed by teleportation
to ensure reliable end-to-end delivery of qubits.
6 CHALLENGES AND REQUIREMENTS
Quantum networks are still in their early infancy. Realising the nec-
essary quantum hardware is of paramount importance and presents
many challenges, but that is only one part of the story. Here, we
present some of the challenges beyond hardware accounting for
the fundamental dierences inherent to quantum communication
and mitigating the limitations and imperfections at the physical
level. Further design considerations can also be found in [15].
Timely decision making. Quantum memory lifetimes are extremely
short even in the most sophisticated setups and this directly impacts
our ability to produce long-distance entanglement by means of en-
tanglement swapping. Entanglement swapping requires that both
entangled pairs of qubits are available on two separate links at the
same time so the intermediate node must be able to store the rst
pair until it receives the second pair. If one of the qubits decoheres,
the pair is lost and the entire process must start over. One approach
to increase the likelihood of such a coincidence event lies in pro-
posals to perform massive multiplexing [
51
] signicantly reducing
the required storage time. There is also the obvious approach of
increasing memory lifetime. NV centres in diamond already exhibit
a high QLE, see Table 1, and lifetimes up to a minute have recently
been observed in NV nodes not yet connected to a network [
6
].
Longer memory lifetimes impose less stringent demands on timing
at the network layer allowing it to be kept at the physical layer.
Nevertheless, mitigating limited qubit lifetimes is essential and
demands fast and reactive control of the network. In a network
based on entanglement swapping it also raises the interesting ques-
tion of whether such entanglement is produced only on-demand, or
if there exists a mechanism which continuously generates entangled
pairs at all times between certain links of the network.
Extending the network stack. In parallel with the eort of building
the physical network links there is a need for work to build up the
quantum network stack vertically. The rst link-layer protocol
has been proposed [
15
]. However, to go beyond point-to-point
connectivity between two directly connected nodes we need a
network layer service and the transport layer to provide platform-
independent services for distributed quantum applications. The
rst end-to-end quantum communication protocols have started to
appear though they generally assume hardware capabilities beyond
what is possible in the near-term future [37, 69].
Routing. In addition to forwarding protocols necessary to actu-
ally generate an end-to-end Bell pair there are many other second-
level mechanisms necessary for a fully functional quantum internet.
The specic question of routing entanglement, i.e. making deci-
sions on how end-to-end entanglement can be established quickly
between users in future quantum networks, is seeing more atten-
tion [
12
,
25
,
26
,
46
,
55
,
63
]. Routing in quantum networks is a non-
trivial problem due to the non-local and temporary nature of en-
tangled pairs as well as dierent physical resource requirements
necessary for delivering these pairs with a high enough delity.
SDN Integration. Given limited lifetimes, building robust and
ecient quantum network routing and management protocols in
an entirely distributed manner may be dicult. This could make
software-dened networking (SDN) a very attractive direction for
quantum networking and has already been considered for QKD [
45
].
SDN is an architecture for programmable networks that splits the
vertical integration of the forwarding and control planes and puts
much of the decision-making capabilities in a centralised controller
(physically decentralised with appropriate redundancy) [
36
]. In this
approach, the central controller has network-wide visibility and
it is responsible for most (or all as is the case for OpenFlow) con-
trol plane decisions based on input it receives from the individual
nodes in the network. It is plausible that in a quantum network a
controller would be responsible for managing the global strategies
for the distribution of long-distance Bell pairs (Bell pairs that have
been produced as a result of entanglement swaps between separate
links), but connection establishment, Bell pair generation, and other
localised operations are left to the actual devices who will try to
conform to the controller’s strategy.
Security. Given that one of the most important features quan-
tum networking brings with it is enhanced security it is crucial
that a design for a future quantum network architecture incorpo-
rates strong security features itself. Such design considerations
should be employed already at the physical layer, to ensure the
protection of quantum network nodes. For example, we remark
that convincing a remote node to produce entanglement with its
neighbour may simply lead to a denial of service attack consuming
its resources [
15
]. This shows that at the very least authentication
is necessary for control messages already at the physical layer. Such
authentication could be realised using standard classical mecha-
nisms, or also use keys generated by QKD in combination with an
information-theoretically secure authentication scheme.
7 CONCLUSION
There is a tremendous amount of work to do to build a fully func-
tional quantum network, both at the physical level and at the sys-
tems and software level. Recent experimental progress in entan-
glement generation rates and memory lifetimes is very promising
and the breadth of the combined research eort should result in
practical demonstrations very soon. Nevertheless, there are a lot
of open questions and research challenges that are unresolved and
require a range of expertise from beyond physics such as operating
systems, computer networks, and communications. This opens up
many new opportunities for researchers from outside the usual
circles to contribute to the growing eld of quantum networking.

NANOCOM ’19, September 25–27, 2019, Dublin, Ireland Wojciech Kozlowski and Stephanie Wehner
ACKNOWLEDGEMENTS
The authors of this memo acknowledge funding received the EU
Flagship on Quantum Technologies, Quantum Internet Alliance,
an ERC Starting Grant (SW) and an NWO VIDI Grant (SW). The
authors would further like to thank [
15
] for permission to reuse
some of their gures.
REFERENCES
[1]
Stefanie Barz, Elham Kashe, Anne Broadbent, Joseph F Fitzsimons, Anton
Zeilinger, and Philip Walther. 2012. Demonstration of blind quantum computing.
science 335, 6066 (2012), 303–308.
[2]
Charles H Bennett and Gilles Brassard. 1984. Quantum cryptography: public key
distribution and coin tossing. In Proceedings of the International Conference on
Computers, Systems and Signal Processing.
[3]
Charles H. Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres,
and William K. Wootters. 1993. Teleporting an unknown quantum state via dual
classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70 (Mar 1993),
1895–1899. Issue 13. https://doi.org/10.1103/PhysRevLett.70.1895
[4]
Hannes Bernien, Bas Hensen, Wolfgang Pfa, Gerwin Koolstra, MS Blok, Lu-
cio Robledo, TH Taminiau, Matthew Markham, DJ Twitchen, Lilian Childress,
and Ronald Hanson. 2013. Heralded entanglement between solid-state qubits
separated by three metres. Nature 497, 7447 (2013), 86.
[5]
Alberto Boaron, Gianluca Boso, Davide Rusca, Cédric Vulliez, Claire Autebert,
Misael Caloz, Matthieu Perrenoud, Gaëtan Gras, Félix Bussières, Ming-Jun Li,
Daniel Nolan, Anthony Martin, and Hugo Zbinden. 2018. Secure quantum key
distribution over 421 km of optical ber. Physical review letters 121, 19 (2018),
190502.
[6]
CE Bradley, J Randall, MH Abobeih, RC Berrevoets, MJ Degen, MA Bakker, M
Markham, DJ Twitchen, and TH Taminiau. 2019. A 10-qubit solid-state spin
register with quantum memory up to one minute. arXiv preprint arXiv:1905.02094
(2019).
[7]
Jürgen Brendel, Nicolas Gisin, Wolfgang Tittel, and Hugo Zbinden. 1999. Pulsed
energy-time entangled twin-photon source for quantum communication. Physical
Review Letters 82, 12 (1999), 2594.
[8]
H-J Briegel, Tommaso Calarco, Dieter Jaksch, Juan Ignacio Cirac, and Peter Zoller.
2000. Quantum computing with neutral atoms. Journal of modern optics 47, 2-3
(2000), 415–451.
[9]
H-J Briegel, Wolfgang Dür, Juan I Cirac, and Peter Zoller. 1998. Quantum re-
peaters: the role of imperfect local operations in quantum communication. Phys-
ical Review Letters 81, 26 (1998), 5932.
[10]
Anne Broadbent, Joseph Fitzsimons, and Elham Kashe. 2009. Universal blind
quantum computation. In 2009 50th Annual IEEE Symposium on Foundations of
Computer Science. IEEE, 517–526.
[11]
C Cabrillo, J Ignacio Cirac, P Garcia-Fernandez, and P Zoller. 1999. Creation of
entangled states of distant atoms by interference. Physical Review A 59, 2 (1999),
1025.
[12]
Marcello Cale. 2017. Optimal routing for quantum networks. IEEE Access 5
(2017), 22299–22312.
[13]
John Clarke and Frank K Wilhelm. 2008. Superconducting quantum bits. Nature
453, 7198 (2008), 1031.
[14]
Rachel Courtland. 2016. China’s 2,000-km quantum link is almost complete
[News]. IEEE Spectrum 53, 11 (2016), 11–12.
[15]
Axel Dahlberg, Matthew Skrzypczyk, Tim Coopmans, Leon Wubben, Filip
Rozpędek, Matteo Pompili, Arian Stolk, Przemysław Pawełczak, Robert Knegjens,
Ronald Hanson, and Stephanie Wehner. 2019. A Link Layer Protocol for Quantum
Networks. arXiv preprint arXiv:1903.09778 (2019).
[16]
Eleni Diamanti, Hoi-Kwong Lo, Bing Qi, and Zhiliang Yuan. 2016. Practical
challenges in quantum key distribution. npj Quantum Information 2 (2016),
16025.
[17]
Anaïs Dréau, Anna Tchebotareva, Aboubakr El Mahdaoui, Cristian Bonato, and
Ronald Hanson. 2018. Quantum frequency conversion of single photons from a
nitrogen-vacancy center in diamond to telecommunication wavelengths. Physical
Review Applied 9, 6 (2018), 064031.
[18]
W Dür, H-J Briegel, JI Cirac, and P Zoller. 1999. Quantum repeaters based on
entanglement purication. Physical Review A 59, 1 (1999), 169.
[19]
Artur K Ekert. 1991. Quantum cryptography based on BellâĂŹs theorem. Physical
review letters 67, 6 (1991), 661.
[20]
A Extance. 2017. Fibre Systems. (2017). Retrieved May 27, 2019 from www.bre-
systems.com/feature/quantum-security
[21]
Joseph F Fitzsimons and Elham Kashe. 2017. Unconditionally veriable blind
quantum computation. Physical Review A 96, 1 (2017), 012303.
[22]
Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone. 2004. Quantum-enhanced
measurements: beating the standard quantum limit. Science 306, 5700 (2004),
1330–1336.
[23]
Daniel Gottesman, Thomas Jennewein, and Sarah Croke. 2012. Longer-baseline
telescopes using quantum repeaters. Physical review letters 109, 7 (2012), 070503.
[24]
Xueshi Guo, Casper R Breum, Johannes Borregaard, Shuro Izumi, Mikkel V
Larsen, Matthias Christandl, Jonas S Neergaard-Nielsen, and Ulrik L Andersen.
2019. Distributed quantum sensing in a continuous variable entangled network.
arXiv preprint arXiv:1905.09408 (2019).
[25]
Laszlo Gyongyosi and Sandor Imre. 2017. Entanglement-gradient routing for
quantum networks. Scientic reports 7, 1 (2017), 14255.
[26] Laszlo Gyongyosi and Sandor Imre. 2018. Decentralized base-graph routing for
the quantum internet. Physical Review A 98, 2 (2018), 022310.
[27]
Hartmut Häner, Christian F Roos, and Rainer Blatt. 2008. Quantum computing
with trapped ions. Physics reports 469, 4 (2008), 155–203.
[28]
Bas Hensen, Hannes Bernien, Anaïs E Dréau, Andreas Reiserer, Norbert Kalb,
Machiel S Blok, Just Ruitenberg, Raymond FL Vermeulen, Raymond N Schouten,
Carlos Abellán, Waldimar Amaya, Valerio Pruneri, Morgan W Mitchell, Michael
Markham, Daniel J Twitchen, David Elkouss, Stephanie Wehner, Tim H Taminiau,
and Ronald Hanson. 2015. Loophole-free Bell inequality violation using electron
spins separated by 1.3 kilometres. Nature 526, 7575 (2015), 682.
[29]
Philip A Hiskett, Danna Rosenberg, Charles G Peterson, Richard J Hughes, S
Nam, AE Lita, AJ Miller, and JE Nordholt. 2006. Long-distance quantum key
distribution in optical bre. New Journal of Physics 8, 9 (2006), 193.
[30]
David Hucul, Ismail V Inlek, Grahame Vittorini, Clayton Crocker, Shantanu
Debnath, Susan M Clark, and Christopher Monroe. 2015. Modular entanglement
of atomic qubits using photons and phonons. Nature Physics 11, 1 (2015), 37.
[31]
Peter C Humphreys, Norbert Kalb, Jaco PJ Morits, Raymond N Schouten, Ray-
mond FL Vermeulen, Daniel J Twitchen, Matthew Markham, and Ronald Hanson.
2018. Deterministic delivery of remote entanglement on a quantum network.
Nature 558, 7709 (2018), 268.
[32]
Takahiro Inagaki, Nobuyuki Matsuda, Osamu Tadanaga, Masaki Asobe, and
Hiroki Takesue. 2013. Entanglement distribution over 300 km of ber. Optics
express 21, 20 (2013), 23241–23249.
[33]
IV Inlek, C Crocker, M Lichtman, K Sosnova, and C Monroe. 2017. Multispecies
trapped-ion node for quantum networking. Physical review letters 118, 25 (2017),
250502.
[34]
Peter Komar, Eric M Kessler, Michael Bishof, Liang Jiang, Anders S Sørensen, Jun
Ye, and Mikhail D Lukin. 2014. A quantum network of clocks. Nature Physics 10,
8 (2014), 582.
[35]
Matthias Körber, Olivier Morin, Stefan Langenfeld, Andreas Neuzner, Stephan
Ritter, and Gerhard Rempe. 2018. Decoherence-protected memory for a single-
photon qubit. Nature Photonics 12, 1 (2018), 18.
[36]
Diego Kreutz, Fernando MV Ramos, Paulo Verissimo, Christian Esteve Rothen-
berg, Siamak Azodolmolky, and Steve Uhlig. 2015. Software-dened networking:
A comprehensive survey. Proc. IEEE 103, 1 (2015), 14–76.
[37]
Takaaki Matsuo, Clément Durand, and Rodney Van Meter. 2019. Quantum link
bootstrapping using a RuleSet-based communication protocol. arXiv preprint
arXiv:1904.08605 (2019).
[38]
Klaus Mattle, Harald Weinfurter, Paul G Kwiat, and Anton Zeilinger. 1996. Dense
coding in experimental quantum communication. Physical Review Letters 76, 25
(1996), 4656.
[39]
M Minder, M Pittaluga, GL Roberts, M Lucamarini, JF Dynes, ZL Yuan, and AJ
Shields. 2019. Experimental quantum key distribution beyond the repeaterless
secret key capacity. Nature Photonics (2019), 1.
[40]
DL Moehring, P Maunz, S Olmschenk, KC Younge, DN Matsukevich, L-M Duan,
and C Monroe. 2007. Entanglement of single-atom quantum bits at a distance.
Nature 449, 7158 (2007), 68.
[41]
William J Munro, Koji Azuma, Kiyoshi Tamaki, and Kae Nemoto. 2015. Inside
quantum repeaters. IEEE Journal of Selected Topics in Quantum Electronics 21, 3
(2015), 78–90.
[42]
Sreraman Muralidharan, Jungsang Kim, Norbert Lütkenhaus, Mikhail D Lukin,
and Liang Jiang. 2014. Ultrafast and fault-tolerant quantum communication
across long distances. Physical review letters 112, 25 (2014), 250501.
[43]
Michael A Nielsen and Isaac L Chuang. 2000. Quantum information and quantum
computation. Cambridge: Cambridge University Press 2, 8 (2000), 23.
[44]
Christian Nölleke, Andreas Neuzner, Andreas Reiserer, Carolin Hahn, Gerhard
Rempe, and Stephan Ritter. 2013. Ecient teleportation between remote single-
atom quantum memories. Physical review letters 110, 14 (2013), 140403.
[45]
Y Ou, E Hugues-Salas, F Ntavou, R Wang, Y Bi, SY Yan, G Kanellos, R Nejabati,
and D Simeonidou. 2018. Field-trial of machine learning-assisted quantum key
distribution (QKD) networking with SDN. In 2018 European Conference on Optical
Communication (ECOC). IEEE, 1–3.
[46]
Mihir Pant, Hari Krovi, Don Towsley, Leandros Tassiulas, Liang Jiang, Prithwish
Basu, Dirk Englund, and Saikat Guha. 2019. Routing entanglement in the quantum
internet. npj Quantum Information 5, 1 (2019), 25.
[47]
M Peev, C Pacher, R Alléaume, C Barreiro, J Bouda, W Boxleitner, T Debuisschert,
E Diamanti, M Dianati, J F Dynes, S Fasel, S Fossier, M FÃijrst, J-D Gautier, O
Gay, N Gisin, P Grangier, A Happe, Y Hasani, M Hentschel, H HÃijbel, G Humer,
T LÃďnger, M Legré, R Lieger, J Lodewyck, T LorÃijnser, N LÃijtkenhaus, A

Towards Large-Scale Quantum Networks NANOCOM ’19, September 25–27, 2019, Dublin, Ireland
Marhold, T Matyus, O Maurhart, L Monat, S Nauerth, J-B Page, A Poppe, E
Querasser, G Ribordy, S Robyr, L Salvail, A W Sharpe, A J Shields, D Stucki, M
Suda, C Tamas, T Themel, R T Thew, Y Thoma, A Treiber, P Trinkler, R Tualle-
Brouri, F Vannel, N Walenta, H Weier, H Weinfurter, I Wimberger, Z L Yuan,
H Zbinden, and A Zeilinger. 2009. The SECOQC quantum key distribution
network in Vienna. New Journal of Physics 11, 7 (jul 2009), 075001. https:
//doi.org/10.1088/1367-2630/11/7/075001
[48] Wolfgang Pfaff, BJ Hensen, Hannes Bernien, Suzanne B van Dam, Machiel S Blok,
Tim H Taminiau, Marijn J Tiggelman, Raymond N Schouten, Matthew Markham,
Daniel J Twitchen, et al. 2014. Unconditional quantum teleportation between
distant solid-state quantum bits.
Science
345, 6196 (2014), 532–535.
[49] Andreas Reiserer and Gerhard Rempe. 2015. Cavity-based quantum networks
with single atoms and optical photons. Reviews of Modern Physics 87, 4 (2015),
1379.
[50] Louis Salvail, Momtchil Peev, Eleni Diamanti, Romain Alléaume, Norbert Lütken-
haus, and Thomas Länger. 2010. Security of trusted repeater quantum key
distribution networks. Journal of Computer Security 18, 1 (2010), 61–87.
[51] Nicolas Sangouard, Christoph Simon, Hugues De Riedmatten, and Nicolas Gisin.
2011. Quantum repeaters based on atomic ensembles and linear optics.
Reviews
of Modern Physics 83, 1 (2011), 33.
[52] N. Raychev, “Quantum Cloning on Macroorganisms
Containing Quantum Information”, Journal of Software
Engineering and Simulation (JSES) (2017)
[53] N. Raychev, “Protocol for stream quantum obfuscation (PSQO)”,
InfoTech-2016 1 (30), 167-174 , (2016)
[54] N. Raychev, “Practical levels of the efficiency, security and reliability
of the quantum cryptographic communication”, InfoTech-2016 1 (30),
167-174, (2016)
[55] N. Raychev, “Logical model for eavesdropping on quantum
encrypted communication”, InfoTech-2016 1 (30), 160-166, (2016)
[56] N. Raychev, “Computational Cluster with Entangled States”, Journal
of Applied Mathematics and Physics 4 (09), 1777, 6 (2016)
[57] N. Raychev, Fundamental Limit for Universal Entanglement
Detection. Journal of Applied Mathematics and Physics, 4, 1567-1577.
doi: 10.4236/jamp.2016.48166 (2016)
[58] N. Raychev. Dynamic simulation of quantum stochastic walk.
International jubilee congress (TU), (2012)
[59] N. Raychev. Classical simulation of quantum algorithms.
International jubilee congress (TU), (2012)
[60] N. Raychev. Interactive environment for implementation and
simulation of quantum algorithms. CompSysTech, DOI:
10.13140/RG.2.1.2984.3362, (2015)
[61] N. Raychev. Reply to "The classical-quantum boundary for
correlations: Discord and related measures". Abstract and Applied
Analysis 11/2014; 94(4): 1455-1465, (2015)
[62] N. Raychev. Reply to "Flexible flow shop scheduling: optimum,
heuristics and artificial intelligence solutions". Expert Systems 2015;
25(12): 98-105, (2015)
[63] T. T. Heikkila, M. Silaev, P. Virtanen, and F. S. Berg-eret, Prog. Surf. Sci.
94, 100540 (2019).
[64] T. Tokuyasu, J. A. Sauls, and D. Rainer, Phys. Rev. B 38, 8823 (1988).
[65] F. Bergeret, A. Volkov, and K. Efetov, Phys. Rev. B 69, 174504 (2004).
[66] E. Strambini, V. Golovach, G. De Simoni, J. Moodera, Bergeret, and F.
Giazotto, Phys. Rev. Mater. 1, 054402 (2017).
[67] M. Wolf, C. Surgers, G. Fischer, and D. Beckmann, Phys. Rev. B 90,
144509 (2014).
[68] Cottet, D. Huertas-Hernando, W. Belzig, and Y. V. Nazarov, Phys. Rev. B
80, 184511 (2009).
[69] N. Raychev. Classical cryptography in quantum context.
Proceedings of the IEEE 10/2012, (2012)
[70] N. Raychev. Bilaterally Symmetrical Transformation between
Independent Operators and Rotations. Journal of Quantum
Information Science, 5, 79-88. doi: 10.4236/jqis.2015.53010, (2015)
[71] N. Raychev. Computational Cluster with Entangled States. Journal of
Applied Mathematics and Physics, 4, 1777-1786. doi:
10.4236/jamp.2016.49183. (2016)
[72] N. Raychev. Bilaterally Symmetrical Transformation between
Independent Operators and Rotations. Journal of Quantum Information
Science, 5, 79-88. doi: 10.4236/jqis.2015.53010. (2015)
[73] N. Raychev. Formalized Operators with Phase Encoding. Journal of
Quantum Information Science, 5, 114-126. doi: 10.4236/jqis.2015.53014.
(2015)
[74] N. Raychev. Formalized Quantum Model for Solving the Eigenfunctions.
Journal of Quantum Information Science, 6, 16-30. doi:
10.4236/jqis.2016.61003. (2016)
[75] N. Raychev. Interactive Quantum Development Environment
(IQDE). Journal of Quantum Information Science, 6, 105-120.
doi: 10.4236/jqis.2016.62010. (2016)
[76] N. Raychev. Logical model for eavesdropping on quantum encrypted
communication, InfoTech-2016, 1, 30, 154-159, 2016, EBSCO Publishing
(2016)
[77] N. Raychev. Practical levels of the efficiency, security and reliability of the
quantum cryptographic communication",InfoTech-2016,1,30,160-
166,2016,EBSCO Publishing (2016)
[78] N. Raychev. Protocol for stream quantum obfuscation (PSQO), InfoTech-
2016,1,30,167-174,2016,EBSCO Publishing (2016)
[79] N. Raychev. Invertibility of Continuous-variable quantum neural
networks based on the Clifford Subsets,IEEE SEM,7,12. (2019)
[80] Nengkun Yu, Ching-Yi Lai, and Li Zhou. 2019. Protocols for Packet
Quantum
Network Intercommunication.
arXiv preprint arXiv:1903.10685
(2019).
[81]
Yong Yu, Fei Ma, Xi-Yu Luo, Bo Jing, Peng-Fei Sun, Ren-Zhou Fang, , Chao-Wei
Yang, Hui Liu, Ming-Yang Zheng, Xiu-Ping Xie, Wei-Jun Zhang, Li-Xing You,
Zhen Wang, Teng-Yun Chen, Qiang Zhang, Xiao-Hui Bao, and Jian-Wei Pan. 2019.
Entanglement of two quantum memories via metropolitan-scale fibers.
arXiv
preprint arXiv:1903.11284 (2019).
[82]
Sebastian Zaske, Andreas Lenhard, Christian A Keßler, Jan Kettler, Christian
Hepp, Carsten Arend, Roland Albrecht, Wolfgang-Michael Schulz, Michael Jetter,
Peter Michler, et al. 2012. Visible-to-telecom quantum frequency conversion of
light from a single quantum emitter.
Physical review letters
109, 14 (2012), 147404.
[83]
Xiaoqing Zhong, Jianyong Hu, Marcos Curty, Li Qian, and H-K Lo. 2019.
Proof-
of-principle experimental demonstration of twin-field type quantum
key distri-
bution. arXiv preprint arXiv:1902.10209 (2019).
[84]
Marek Zukowski, Anton Zeilinger, Michael A Horne, and Aarthur K Ekert.
1993.
Event-ready-detectors”Bell experiment via entanglement swapping.
Physical
Review Letters 71 (1993), 4287–4290.