# Packet Switching in Quantum Networks: A Path to Quantum Internet

Stephen DiAdamo<EMAIL_ADDRESS>Cisco Research, Garching bei München,
Germany  Bing Qi<EMAIL_ADDRESS>Cisco Research, Los Angeles, CA, USA  Glen
Miller  Acacia Communications, Mass-Scale Infrastructure Group, Cisco,
Maynard, MA, USA  Ramana Kompella  Cisco Research, San Jose, CA, USA  Alireza
Shabani<EMAIL_ADDRESS>Cisco Research, Los Angeles, CA, USA

(May 16, 2022)

###### Abstract

Large-scale quantum networks with thousands of nodes require scalable network
protocols and physical hardware to realize. In this work, we introduce packet
switching as a new paradigm for quantum data transmission in both future and
near-term quantum networks. We propose a classical-quantum data frame
structure and explore methods of frame generation and processing. Further, we
present conceptual designs for a quantum reconfigurable optical add-drop
multiplexer to realize the proposed transmission scheme. Packet switching
allows for a universal design for a next generation Internet where classical
and quantum data share the same network protocols and infrastructure. In this
new quantum networking paradigm, entanglement distribution, as with quantum
key distribution, is an application built on top of the quantum network rather
than as a network designed especially for those purposes. For analysis of the
network model, we simulate the feasibility of quantum packet switching for
some preliminary models of quantum key and entanglement distribution. Finally,
we discuss how our model can be integrated with other network models toward a
realization of a quantum Internet.

##  I Introduction

Quantum computing, networking (communication), and sensing are emerging as
frontier technologies for information processing. Quantum computers can offer
better solutions to hard problems in chemistry and material science [1, 2], as
well as in machine learning [3, 4]. Quantum networks enable quantum-secure
communication [5, 6] and entanglement-assisted communication [7], while higher
measurement sensitivity can be achieved with quantum sensors [8]. Among
quantum information technologies, quantum networking in particular is finding
a more central role. Beyond communication and cryptography related
applications, quantum networking can be a key part of developing large-scale
quantum computers via interconnecting multiple quantum chips [9, 10, 11].
Also, networked quantum sensors exchanging quantum information collectively
have stronger sensing power [12, 13].

One can envision for the future thousands, or even millions, of devices
connected over a global quantum network of networks—namely, a quantum
Internet. Which networking infrastructure and protocols can allow for the
realization of such a large-scale quantum network? Despite previous proposals
[14] there has been no comprehensive answer to this question and proposals for
quantum networking protocols and network layers have been limited to
particular applications such as entanglement distribution [15, 16, 17] or
quantum key distribution (QKD) [18]. Also from the infrastructure perspective,
there has been a quest for classical and quantum network coexistence [19, 20,
21], although with no clear coexisting protocols or network specifications. In
this paper, we introduce a packet-switched quantum network as an answer to the
above question. Before presenting our proposal for packet switching it is
important to discuss the bigger picture and how we conclude packet switching
as the path forward. We start by introducing the following basic engineering
principals which need consideration when designing a large-scale quantum
network, and specifically, a quantum Internet:

1) _Universality:_ We define a universal quantum network as one which can
accommodate any application, and not just those which rely on entanglement
distribution [15, 16, 17]. A prominent example is the BB84 prepare-and-measure
QKD protocol [22] which does not require any entanglement resources. In this
regard, a future quantum Internet should serve all users universally,
independent of the use case. Correspondingly, quantum networking protocols and
layers should serve any application whether it is QKD, entanglement
distribution, blind computing [23], or any other application. Note that here
we consider entanglement distribution (and correspondingly teleportation) as
an application rather than a layer of quantum networks.

2) _Transparency:_ Quantum networks can use the same physical media as
classical optical networks for data transmission, whether optical fiber or
free space links. Although quantum networking experiments often employ
separate fibers for classical and quantum signals, we consider any realistic
field deployment to rely on the coexistence of classical and quantum signal
over the same medium. Furthermore, we assume as an engineering principle that
future Internet protocols should function regardless of the nature of
transferred data, whether it is classical or quantum. Therefore, we believe
quantum-classical coexistence is not merely sharing the same physical media
[19] but sharing the same network routing protocols, layers, and standards.

3) _Scalability_ : The quantum networking protocols should be able to support
the growth of the network. In the classical world, the primary reason for the
development of packet switching in telecommunication systems was to
accommodate the growing number of users and need for high-bandwidth
communication. Packet switching allows easier network management, dynamic
correction for the points of failure, and better use of physical
infrastructure. Moreover, much of the success of classical communication
networks can be accredited to the standardization approaches used for scaling
and interoperability. With standardization, networks composed of software and
hardware developed by various vendors can be integrated into existing networks
with performance guarantees at very little effort. We therefore believe with
an early adoption of packet switching for quantum networks, we prevent a later
transition from a collection of switching approaches seen today to one which
can allow for easier standardization, using the same already-carved path
classical networks used.

We consider universally, transparency, and scalability as three design
principals for a quantum Internet, or simply the design principles for the
future Internet. In this work, we introduce packet switching as a quantum
networking paradigm that satisfies these principles.

This article is organized as follows: in Section II, we introduce our approach
to packet switching in an optical quantum network, also introducing our
classical-quantum hybrid frame structure and a proposal for optical network
hardware to implement the approach in Section III. In Section IV, we
investigate two example use-cases for our network model, namely quantum key
and entanglement distribution, appropriate for a near-term implementation of
our network model. In Section V, we investigate how our network model can be
integrated with currently deployed optical networks and moreover with
currently deployed or proposed quantum networks. The paper is concluded in
Section VI along with final discussion and outlook.

##  II Packet Switching for Optical Quantum Networks

The first communication networks installed commercially relied on the concept
of circuit switching in order to route data packets in the network [24]. At a
high level, circuit switching is a switching approach that, given a route in a
network, reserves the entire capacity of the channels in the route until
communication is terminated. Indeed in some situations, circuit switching can
provide advantages, such as maintaining synchronization, low latency
transmissions, and overall simplicity. One major downside of circuit switching
was that in scenarios of bursty network traffic, the communication channels
could often be reserved with little to no traffic being transmitted. To
improve the utilization of the network, and to aid in accommodating the
growing number of network users, the concept of packet switching was widely
adopted [24].

Given that the concept of quantum networks is in a very early stage of
development, there has not yet been much consideration on how to handle many
users in the network. In particular, of the current proposals for quantum
networks, there has not been an equivalent design proposed analogous to packet
switching. Indeed currently deployed quantum networks need only to support
very few users and can only supply low communication rates. The largest
reported entanglement-based QKD network for distributing quantum keys without
trusted nodes was demonstrated in [25], supporting 8 unique users with a
average of 1 kb/s of secure key in the best case. The approach used in [25]
was not a routing approach with packet switching in a networking sense, but
rather an assignment of unique wavelengths assigned for each user allowing for
communication between any two users, essentially dedicating a direct
communication line between pairs of users. In this sense, the 8-user network
forms a complete network such that no link-layer functionality for switching
is involved. In [26], a 46-node QKD network is demonstrated with switches and
trusted nodes at 49.5 kb/s, and in the work, a circuit-switched approach is
used.

For future quantum networks, we believe packet switching will allow for many
users as well as support higher communication rates, but the construction of
such a system will naturally come with its own challenges. The implementation
of packet switching in quantum networks can be largely inspired by classical
optical networks, but indeed there are major challenges to overcome due to the
nature of quantum systems in comparison to purely classical systems. In
optical networks, it is common that when a packet arrives, the control
information and payload of the packet is converted from the optical domain
into the electrical domain. This implies the optical signal is measured and
converted into a computer-readable format. When the packet is ready for
retransmission, the payload is converted back into the optical domain and sent
onward through the next fiber. This process is known as O/E/O conversion.
During this waiting time, the payload information can be stored essentially
for as long as necessary without any deterioration to the signal, and moreover
the information can be corrected for any errors. As network traffic rates
increased, and because the operation of converting optical signals to
electrical signals was—and in some cases still is—expensive to perform, or the
computational power was missing, methods for keeping the payload information
in the optical domain were introduced [27, Chapter 13]. Devices such as
optical switches, wavelength selective switches, reconfigurable add drop
multiplexers, and other optical components were invented [28]. The problem
with these devices is that they further attenuate the signal. With classical
information, the payload signal can be amplified to mitigate signal
attenuation due to the components, maintaining a strong signal for the next
transmission in the route [28].

In the quantum case, many of these solutions do not carry over. The nature of
quantum mechanics is such that arbitrary quantum states cannot be measured to
then be regenerated in the same state. Quantum states can be in a
superposition of states and measuring the system forces it to collapse into
one basis state, destroying the superposition and thereby any encoded quantum
information. Without the full knowledge of the quantum state before
measurement, the state cannot be perfectly regenerated, and so conversion of a
quantum state to the classical domain is not possible. This prevents us from
using classical data storage and error correction approaches. Indeed with
optical memories [29, 30], a similar approach could be considered. Another
problem to overcome is that quantum states are very fragile, and storing them
in memories can rapidly cause the decoherence of the quantum state, ruining
the encoded information. Moreover, the writing and reading steps for storing
and retrieving a quantum state from memory can cause additional loss on an
already inherently weak quantum signal. With these known effects, the amount
of time that a quantum state remains in a memory should be minimized.

Performing error correction on a quantum state while it is in memory could
also be possible, but would require a quantum computer capable of performing
the necessary operations, a technology that is expected in the future. This
level of technology is essentially an all-optical quantum repeater [31]. Using
the hardware components for all-optical classical networks is the more near-
term approach to overcoming issues with storing quantum systems, but another
hurdle exists that is non-trivial to overcome. Many existing optical network
technologies rely on signal amplification to overcome attenuation effects.
Because arbitrary quantum states cannot be copied [32, 33], amplifying weak
quantum signals is not a possible method for overcoming attenuation.
Therefore, one would need to construct low-loss optical hardware for improving
the performance and reliability of the network.

Optical communication is the backbone of telecommunication systems, where data
is encoded into laser pulses and transferred over optical fibers or free
space. In its current form, optical communication is not purely optical as it
transforms back and forth into the electrical domain at intermediate nodes for
error correction and amplification [27, Chapter 13]. In early days of optical
communication, building an all-optical network where data stays in optical
domain all along the network was a goal [28]. Realizing an all-optical network
remains an unachievable goal due to challenges not much different from what we
face in quantum networks, where the main difference is that instead of the
strong light signals used in classical communications, we have weak light
signals that cannot be copied. Although a rather obsolete field, we can still
learn from the older works in this area.

Overall, the path to building large-scale quantum networks capable of
supporting a large number of users will require both the invention of new
technology as well as optimizing current technology to accommodate the
challenges of transporting quantum systems. With these challenges in mind, we
present an approach to packet-switched quantum networks that is both future-
proof, accounting for the arrival of novel quantum technologies, as well as
timely, in the sense that in the near-term our approach can already be used to
deploy some quantum networking applications. In this section, we aim to learn
from history and thus define a packet switching approach preemptively to
prepare for the coming of large-scale quantum networks, supporting the
deployment of many quantum network applications as well as many users.

###  II.1 Classical-Quantum Hybrid Frame Structure

In order to perform packet-switching in a quantum network, we need to firstly
define a data frame structure capable of handling a quantum payload. The
central idea we use is a hybrid frame structure: each quantum payload is
framed with a classical header and trailer. The header contains crucial
information for routing, error mitigation and correction. The trailer
indicates the end of the quantum signal as seen in Fig. 1. The classical
header and trailer and the quantum payload can be generated using different
photonic sources and multiplexed into a hybrid data frame by using a different
degree of freedom of light, such as time, wavelength, polarization, spatial
mode, and so on, or any combinations of them, as shown in Fig. 2.

Figure 1: Quantum frame structure. The frame is composed of three components:
A classical header, a quantum payload, and a classical trailer.

In Fig. 2 (a) is a depiction of a source node which generates a hybrid frame.
A control unit is used to trigger hardware components that generate signals
for the classical header and trailer as well as the quantum payload. The
classical transmitter encodes the header and trailer data and a quantum source
emits and encodes quantum states. The two signals are then multiplexed using
some predetermined form of multiplexing and sent through the fiber. The
quantum source depicted is a general source and can emit arbitrary quantum
states, even multi-mode systems. In the figure, we do not depict the trailer
portion of the frame, but the trailer will follow the quantum payload as
depicted in Fig. 1 using the same encoding and multiplexing as the header.
Fig. 2 (b) is a depiction of two multiplexing approaches. On the left is time
division multiplexing, where the header information will be sent earlier in
time than the quantum payload, so that the receiver can distinguish the two.
On the right is wavelength division multiplexing, where the signals can be
sent simultaneously but at different wavelengths.

Figure 2: Hybrid frame generation. (a) The classical header and quantum
payload can be generated from different photon sources and multiplexed into a
hybrid data frame using a MUX. (b) Two examples of multiplexing schemes: time-
division multiplexing (TDM) and wavelength-division multiplexing (WDM).

In our proposal for a quantum network data frame, we modify the contents of
the header and trailer to attempt to accommodate the uniquely-quantum noise
effects that arise. In this preliminary work, it is difficult to plan for the
coming novel technologies surrounding quantum networks. As a first step, we
modify the standard Link-Layer Discovery Protocol frame (LLDP) [34] to
accommodate quantum data transmission, forming a quantum Ethernet frame. The
motivation behind this is that LLDP frames are widely used and integrated with
existing switching hardware. Moreover, LLDP frames have flexibility to add
additional fields for switching choices and error correction. The general
contents of our frame header are much like a traditional frame, it should
contain information regarding the source and destination and specific control
codes. On top of the parts found in standard LLDP frames, we add additional
fields to the Type-Length-Value (TLV) part of the frame that are specifically
quantum. In this stage of development, fields we imagine will be the details
surrounding quantum error correction and mitigation. Data such as how long the
quantum payload has spent in a quantum memory, a maximum cut-off time until
the frame is dropped, and the quantum error correction protocol to be used for
error correction should be integrated. For the trailer, we use the same frame
structure with a binary value in a Header/Trailer TLV to distinguish the two.
We detail the frame in Table 1. At this stage, we imagine the trailer will
simply indicate the end of the signal, but future iterations could integrate
trailer structures that incorporate additional resources for quantum channel
estimation [35], or other error correction information for example. Future
work will be to form concrete structures for the header and trailer to work in
a completely general setting.

Table 1: The modified LLDP frame structure for quantum data transmission. Here
we add additional Type-Length-Value (TLV) data for quantum and consider a
Quantum Data Unit (QDU).

###  II.2 The Approach to Packet Switching

With a frame structure defined, the question of how a frame is transmitted and
processed at relay nodes is next to be considered. We have discussed how the
classical and quantum information can be multiplexed, but how a frame is
logically processed and the type of hardware available at each relay switch
can dictate the precise timing of the frame generation. In a classical
setting, because it is possible to amplify, copy, and correct errors, the
precision of timing for when the parts of a frame are transmitted is less
critical—a frame payload can be sent with its header shortly in front of it
with a closely following trailer. With quantum information, because of the
complexity involved in transporting and storing it, precise timing and
synchronization are critical. For this, we propose the use of two switching
schemes based on classical schemes used in optical networks.

Technology for quantum memories is in a very early stage of development and
the capability of the memories for maintaining quantum state fidelity is
generally in the millisecond to low single digit seconds range, especially
lower in systems coupled to networks [36, 37]. We therefore propose a near-
term approach that makes no use of quantum memory, appropriate for an initial
implementation stage of our quantum network model. Our scheme is based on a
switching scheme known as burst switching, or “just-in-time” switching. The
idea here is, given roughly the number of hops from source to destination, to
add enough guard time—the time between when the header is transmitted and when
the quantum payload is transmitted—such that at each node, a routing decision
can be made before the payload arrives. Once the payload arrives, if
processing is complete, then the payload can be sent onward. If processing is
not complete, or the node is not able to handle the frame, the payload is
discarded and a retransmission can be made with more guard time. Depicted in
Fig. 3 is an example of burst switching. In a sense, this approach is a hybrid
approach between packet switching and circuit switching. The benefit gained in
this case over circuit switching is that dynamic routing is still possible.
This additional freedom can therefore allow for better network utilization.

Figure 3: An example of burst switching. A frame is sent from node $S$ to node
$D$ in the network with the header part of the frame (solid) sent $\delta_{0}$
seconds earlier than the payload. Once the frame passes through node $1$, the
time-gap between the header and the payload decreased to a time difference of
$\delta_{1}<\delta_{0}$, due to the processing delay at node $1$. This repeats
at node $2$ and at the destination $D$, where the frame is dropped from the
network.

In the next case, we assume the network nodes are capable of storing quantum
payloads. Depicted in Fig. 4 shows an initial hardware concept. In this case,
we do not require as precise a guard time, and the stronger the memory, the
weaker the precision needs to be. When the header arrives at a node, if by the
time the payload arrives the node is busy, the payload will be switched into a
quantum memory to be stored until transmission becomes possible. Here, for
example, a node can make use of the optional parameters of the proposed
quantum Ethernet frame that can state a maximum storage time for the quantum
payload before it should be dropped. If the payload requires a higher fidelity
and the maximum duration for storage has elapsed, the payload can be dropped.

In both cases, while the classical header and trailer can be amplified,
measured, and regenerated at each network router, the quantum payload should
be transmitted through the entire network faithfully without being measured or
amplified at the intermediate network nodes. Our proposals are conceptually
similar to the photonic packet switching in classical all-optical networks
[38, 39], so there are some common challenges in both quantum and classical
schemes. We will explore ways to overcome these challenges in detail in future
work.

##  III Network Hardware Requirements for Packet Switching

With the frame processing defined in the previous section, we explore concepts
for the physical hardware capable of processing the hybrid frames. One key
building block of packet-switched quantum networks is a quantum version of
Reconfigurable Optical Add Drop Multiplexer (ROADM)—a q-ROADM—which acts as a
quantum switch able to route quantum information through a large network. We
remark that a QKD network using a modified classical ROADM has been
demonstrated recently [40], where the authors bypassed the optical
amplification unit and reduced the insertion loss for the QKD signals. While
this approach can be useful in near-term applications like QKD, it is not
adequate for a general-purpose quantum network due to the lack of crucial
quantum functionalities such as payload storage and dynamic switching.
Furthermore, it is designed for circuit-switched networks, rather than packet-
switched networks discussed in this paper.

In this section, we consider two paths to realizing a hardware capable of
processing the classical-quantum hybrid frames. On one path, we aim for a
near-term solution, capable of processing a frame with limited additional
functionality, and on the other, a longer-term design with additional
components that will make the network more robust and efficient. In the first
case we target only the essential features required to process the frame,
ignoring error correction, signal frequency conversion, or any other
optimizations that can complicate the system. We depict the hardware design in
Fig. 4. In this case, the multiplexed classical-quantum frame enters a de-
multiplexer to separate the header information from the payload. The header
enters a processor, and the quantum payload a memory. The memory in this case
can be a delay line or a more robust optical memory. The classical information
is processed to determine when to release the quantum payload and then is
regenerated and multiplexed with the payload. The multiplexed frame is sent
through an optical switch to be sent to the next destination, along with the
classical trailer following, processed the same way as the header. In general,
in this setting the transmission protocols should be designed with very
limited quantum memory abilities in mind, as explained in the previous
section.

For the second, more distant future, path, inspired by the classical ROADM, a
conceptual design of a q-ROADM is shown in Fig. 5. This design incorporates
more complex components that can achieve error correction and signal frequency
conversion. It also is designed to handle many users. Here, a q-ROADM can have
multiple input fibers, output fibers, and add/drop channels, similar to a
classical ROADM. Each fiber may carry multiple wavelength channels. Depending
on the multiplexing scheme employed, a corresponding de-multiplexing is used
to separate the classical header and the quantum payload. After being
optically amplified and converted into electrical signals, the classical
information contained in the header will be fed into a control unit, to decide
how to further process the quantum payload. In the meantime, the quantum
payload will be stored in quantum memory (q-Memory), and the classical trailer
will arrive, following the same path as the header. Depending on the
application, quantum error correction or other quantum operations may be
performed on the quantum payload by the q-Processor. Based on the state of
network traffic, the control unit will determine the optimal output, and
provide control signals to release the quantum payload from q-Buffer and
perform wavelength conversion if needed. It also regenerates the classical
parts of the frame at the suitable wavelength and provides the control signal
to the optical switch fabric to multiplex the header with the quantum payload
and route the hybrid data frame to the suitable output fiber.

A fully functional, general-purpose, q-ROADM for a packet-switched quantum
network may require significant breakthroughs for many fundamental quantum
technologies, such as long-lived quantum memory and quantum repeaters. In the
meantime, we can make use of near-term technologies and trade-off with a focus
more on the timing and synchronization in order to make do with presently
available hardware. Indeed, with a near-term approach, we cannot overcome the
attenuation effects of the optical components. As discussed earlier, quantum
networking has its unique challenge associated with the quantum no-cloning
theorem [32, 33], where an arbitrary unknown quantum state cannot be perfectly
cloned. This implies that, with the exception of some loss-tolerant protocols
like QKD, quantum repeaters [41] capable of distant entanglement generation or
error correction are required for constructing general-purpose large-scale
quantum networks.

Figure 4: A first iteration device for quantum frame processing and switching.
The classical-quantum hybrid frames enter a demultiplexer and the header
(solid) is split from the quantum payload (dotted) via an Optical Switch (OS).
The header is processed into an electrical domain and the information used to
determine the next hop. Once determined, the quantum payload is released from
the q-Memory, merged with the header by another OS, multiplexed with the other
frames, and sent onward. Figure 5: A conceptual design of a quantum ROADM.
From the left side, $N$ fibers containing multiplexed frames enter a
demultiplexer to separate the classical header information from the quantum
payload. The classical header if processed in the Control and the quantum
payload sent to a quantum processing unit. In the quantum processing unit, the
quantum payload is stored, corrected of errors, and if needed, undergoes
frequency conversion. Once ready for transport, the payload travels through
optical switch fabric and it output behind its regenerated header.

##  IV Example Applications Built on Packet-Switched Quantum Networks

In the near term, without the ability to store quantum information for long
periods nor the ability to perform robust quantum processing, overcoming the
effects of loss for long distance quantum communication is not possible for
arbitrary quantum states. There are, however, some applications that can still
function under heavy loss. In this section, we explore an initial analysis of
two such applications; quantum key distribution and entanglement distribution.

###  IV.1 Quantum Key Distribution

One of the most mature quantum communications protocols is Quantum Key
Distribution (QKD). QKD is a protocol that allows two remote users (e.g. Alice
and Bob) to establish a secret key using an untrusted quantum channel and an
authenticated classical channel [5, 6]. The generated secret key can be
further applied in various cryptographic protocols to achieve information-
theoretic security, using encryption schemes like the one-time-pad.
Alternatively, other secure encryption schemes like the Advanced Encryption
Standard (AES) [42], which requires less key material generally consuming 128
or 256 bits, and refreshing periodically, could be employed.

There are two key features that make QKD much easier to implement than other
quantum network protocols, which can require transferring arbitrary quantum
states, such as distributed quantum computing. First, most QKD protocols are
loss-tolerant in the sense that a secret key can still be generated even when
most of the transmitted photons are lost in transmission [5, 6]. This suggests
that the storage of QKD signals in a network switch may not be necessary and
moreover can be routed through imperfect optical devices such as optical
switches. Second, most QKD protocols are noise-tolerate in the sense that
secret key material can be generated from quantum signals of relatively low
fidelity by performing classical error correction and privacy amplification.

So far, all existing QKD demonstrations have been based on the circuit
switching scheme, where a dedicated quantum link is established between the
sender and receiver before quantum transmission starts. However, such a scheme
may not be efficient in a large-scale quantum network in a similar way as was
experienced with early telephone communication networks. As discussed in
Section II, a hybrid quantum-classical data frame could be constructed by
adding a classical header (trailer) in front of (behind) the quantum payload.
On one hand, the classical header is structured to carry information such as
the network addresses of the sender and the receiver, the data structure of
the quantum payload, etc., and can be measured, processed, and regenerated at
intermediate networks nodes. On the other hand, to maximize the QKD
performance, disturbance to the quantum payload should be minimized along the
quantum channel and at the network nodes.

We remark that the security of QKD is not dependent on the details of the
quantum channel or routing algorithms. In fact, in standard QKD security
proofs, the quantum channel is assumed to be fully controlled by the adversity
(Eve). This is convenient because we do not need to develop a new security
proof for packet-switched QKD networks. Nevertheless, the performance of QKD,
in terms of secret key rate and QKD distance, is highly dependent on both the
quantum channel characteristics and routing strategies. It is therefore
important to conduct numerical simulations to study the performance of QKD in
different network configurations.

Among various QKD protocols, in this paper, we study a representative prepare-
and-measure protocol, namely the BB84 protocol [22]. The central idea can also
be applied to other QKD protocols, such as entanglement-based QKD [43],
measurement-device-independent QKD [44], and others. More specifically, we
consider the polarization encoding BB84 QKD, where Alice prepares single-
photon states with polarization randomly chosen from $\\{H,V,D,A\\}$, where
$H$ ($V$) refers to horizontal (vertical) polarization state and represents
bit $0$ ($1$) in the rectilinear ($Z$) basis, while $D$ ($A$) represents $45$
($135$) degree polarization state and represents bit $0$ ($1$) in the diagonal
($X$) basis.

For transmission, Alice, the sender, labels $k$ encoded single-photon pulses
into a frame by adding a classical header, emitting the $k$ photons, adding
the trailer, and proceeds to send the hybrid data frame to Bob, the receiver,
through a packet-switched quantum network. Alice repeats the above process,
until all $m$ desired frames are transmitted. At Bob’s end, he processes the
classical header and trailer and the quantum payload separately. The classical
parts of the frame can be measured with a classical detector and provide Bob
with the information about the sender and the quantum payload. The
polarization of each photon in the quantum payload is then measured in a
randomly chosen basis. After the $m$ frames have been registered, or a maximum
QKD session time has been reached, Bob informs Alice and they start the post-
processing protocol using a classical authenticated channel, which could be
over a separate classical network, or in our vision of quantum networks, over
the same channel.

In the classical post-processing stage, Alice and Bob use data collected in
$X$ basis to upper bound Eve’s information and data collected in the $Z$ basis
for secret key generation. For simplicity, we further assume that Alice has a
perfect single photon source. The asymptotic secret key rate (per
transmission) for the efficient BB84 QKD protocol [45] is given by,

$R=KQ[1-f\cdot H_{2}(e_{Z})-H_{2}(e_{X})],$ (1)

where $Q\in[0,1]$ is the gain, $e_{Z}$ and $e_{X}$ are Quantum Bit Error Rate
(QBER) in $Z$ and $X$ basis correspondingly, and
$H_{2}(x)=-x\log_{2}(x)-(1-x)\log_{2}(1-x)$ is the binary Shannon entropy
function. The parameter $f$ quantifies the inefficiency of the classical key
reconciliation process. Here, we also introduce a parameter $K\in[0,1]$, which
quantifies the data loss due to the routing strategy, as will be discussed
below.

In a real QKD process, all the parameters in Eq. (1) can be estimated from
experimental results without any knowledge about the quantum channel. However,
to estimate the QKD performance by numerical simulation, we establish a
theoretical model to describe both the QKD system and the quantum channel. The
model depends on both the network configuration and the routing algorithm. As
an illustrative example, we consider a simple network configuration, where the
two QKD users are connected by a single path with $n$ intermediate switches,
as shown in Fig. 6. In this analysis, we assume the switches are early-stage
quantum switches and have no quantum memories, and therefore no storage
ability. Each switch can separate the classical parts of the frame and quantum
payload, read out the classical information, regenerate the classical header
and trailer, and detour the quantum payload to the outgoing channel if
available. To introduce some network dynamics, we assume the outgoing channel
at each switch is available with a probability of $P$ when the QKD signal
arrives.

Figure 6: A simple network configuration for QKD simulation. The sender has a
Single Photon Source (SPS) which leads into an encoding device which prepends
header information and appends a trailer information. The frame is encoded
according the BB84 protocol in this scenario. The encoded frame is then sent
into the network where it will travel through a number of switches. At each
switch there is a probability of data drop due to network contention and some
loss due to the header processing time. Eventually, the frame arrives at the
receiver where the standard BB84 decoding scheme is performed using a basis
selection device which directs photons to one of the two Single Photon
Detector (SPD).

We adopt a simple routing strategy as follows: (1) If the channel is
available, the quantum payload goes through with a fraction of loss
corresponding to the processing time of classical header; (2) If the channel
is not available, the whole quantum payload is discarded. It is easy to show
the factor $K$ in Eq. (1) is given by,

$K=P^{n}\dfrac{T_{Q}-nT_{P}}{T_{Q}},$ (2)

where $T_{Q}$ is the temporal length of the quantum payload, and $T_{P}$ is
the processing time of the classical header at each node.

With this model, we determine the secret key rate for a varying number of mid-
way switches and an independent length parameter $L$. The simulation results
of the secret key rate as a function of the total channel length for different
$n$ are shown in Fig. 7. Here we assume the quantum channels are single-mode
fibers with an attenuation coefficient of $0.2$ dB/km. Other simulation
parameters are as follows: the detector efficiency is set to $0.5$; the
detector dark count probability is $10^{-6}$; $f=1.15$; $T_{Q}=100\cdot
T_{P}$; and $P=0.5$. The first three are typical values in QKD demonstrations.
To reduce the data loss due to the processing time of classical header, we
choose a relatively large ratio of $T_{Q}/T_{P}$. The simulation results
suggest that it is possible to conduct QKD over packet-switched network
without using quantum memory. We remark that in a more complicated network
setup, the QKD performance could be further improved by storing the quantum
payload at the switch when the outgoing channel is not available. We leave
this scenario as a future research for this application, and explore it
further in the next section with entanglement distribution.

Figure 7: The secret key rates of QKD over a packet-switched quantum network
without quantum memories. $n$ is the number of hops. The decrease of the
secret key rate with the increase of $n$ is due to the data loss at the
routers. The case of $n=0$ is equivalent to circuit switching.

###  IV.2 Entanglement Distribution

Entanglement distribution is another key application enabled by quantum
networks. Quantum entanglement is a resource that can be directly used in
various ways to perform particular quantum tasks like quantum state
teleportation [46] and entanglement based quantum key distribution protocols
[43]. Moreover, entanglement can be used as a supplemental resource within
protocols to boost the performance, such as in entanglement-assisted
communication [47] or various multi-party nonlocal games, one well known
example being the CHSH game [48]. Entanglement alone cannot be used to
transmit information—known as the no-communication theorem—but used as a
resource, can be used to enable quantum communication at large scale [15].

An entanglement resource is composed of multiple quantum systems, each part of
which sharing a correlation with the other parts. The task of distributing
entanglement is therefore to transfer each communicating party a piece of the
entangled system. Once transferred, they can use the entanglement as they
like, to perform quantum teleportation, entanglement swapping for extending
the reach of an entangled pair [49], an entanglement-based QKD, or any other
protocol where entanglement is used. Entanglement, similarly as discussed with
QKD resources, is a resource that when lost in transmission has little
consequence—another entangled system can be generated and the distribution
reattempted. Also, since entanglement alone contains no information by itself,
and due to the monogamy of entanglement [50], losing the resource cannot leak
any secret information or correlation to potentially malicious third parties.

Along the same lines of the previous subsection, we analyze how well hybrid
classical-quantum frames composed of entangled systems as payloads can be
transmitted over packet-switched quantum networks. The entanglement we
consider in this initial work are Einstein-Podolsky-Rosen (EPR) pairs. EPR
pairs are two-qubit, maximally entangled qubits, meaning they are perfectly
correlated (or anti-correlated) in measurement outcome. To quantify the
entanglement-distribution ability of a packet-switched quantum network, we use
the entanglement fidelity as a metric, measuring the fidelity in various
network settings to observe the hop-by-hop noise effects. In simulation, the
fidelity can be calculated numerically without statistical fluctuation, but
naturally in an experimental setting would require more effort. Nonetheless,
as a preliminary step, simulating the noise effects plays an important role
for taking the first steps towards realizing a packet-switched quantum network
able to distribute quantum entanglement.

Related to this section are two prior works that investigate the memory
effects on the ability to distribute quantum entanglement. Instead of an
approach based on optical switching, the two works [51, 52] use an approach of
creating pair-wise entanglement and performing entanglement swapping. In [51],
Kozlowski et al. consider a network-layer protocol for managing the
distribution process in a quantum network, where the hardware parameters are
near-term parameters. The authors also use NetSquid, as we do, to demonstrate
their protocol. Their protocol firstly establishes a virtual circuit between
the sender and receiver and once a virtual circuit is established, no further
routing is required. Since the protocol uses entanglement swapping as the
basis for distributing entanglement, switching frames of quantum systems is
not considered. In [52], Semenenko et. al consider how varying memory
lifetimes affects the entanglement generation rate in a linear chain of nodes,
again, distributed via entanglement swapping, not using a packet-switching
approach as we do here.

For this simulation analysis, we determine how well the entanglement fidelity
is maintained after halves of EPR pairs, a collection of which forming a frame
payload, are sent through the network in various parameter regimes and network
configurations. In terms of node capabilities, we use a similar configuration
as in the previous section in Fig. 6 except in this case, we allow the nodes
in the network to have quantum memories, and the source here emits entangled
pairs in two spatial modes. We consider two scenarios for entanglement
distribution. In the first case, entanglement is generated at a central node
and one half of each pair is sent to a respective receiver, as depicted in
Fig. 8 (a). In this case, each path has its own hybrid frames individually
prepared, and both end-nodes act as a receiver. We assume the two output paths
of the quantum source act as individual quantum sources with respect to Fig. 2
(a). We depict the setting in Fig. 9, where each path gets its own header and
trailer information. One can further imagine entanglement sources that output
more than bipartite entanglement, extending the same concept to many output
fibers. In the second case depicted in Fig. 8 (b), the entangled pair is
generated at the sender. In this case, one half of the entangled pair is
stored in a quantum memory, and the other part is sent through the network
through a linear chain of nodes to a specific destination a varying number of
hops away.

The switching approach we use in this case is similar to that of the previous
section, except in this case we simulate a header processing delay which
delays the forwarding of any arriving qubits for the time between the header
arrival to a later time when the header information is processed. Each node
has a defined processing delay so that it does not forward any arriving qubits
during this time. In practice, the qubits that do arrive during the processing
time are stored in a memory, but those arriving after the processing time
travel through to the next hop in the path without entering the memory. In
this simulation, the minimum storage time is the time a full frame takes to
arrive. When one half of an entangled pair reaches a receiver, the fidelity of
the pair is computed. In practice, the entanglement units could be stored to
perform quantum teleportation for example, which we plan to analyze more
deeply in future work.

To create the simulation according to the above specifications, we use the
quantum network simulation platform NetSquid [53]. NetSquid is a discrete
event simulation tool that can be used for simulating complex quantum
networks. The simulated nodes in the network can have various components such
as quantum sources, detectors, memories, processors, and channel models such
as optical fiber. Each component used in NetSquid has a physical model
attached to it so to simulate noise and loss in a realistic way.

To implement the behavior of the nodes, we implement the necessary protocols
in the language of NetSquid. At a high level, the three key protocols we
implement are a frame-sending protocol, a frame-relaying protocol, and a
frame-receiving protocol. The frame-sending protocol generates qubits from—in
this case—a perfect quantum source, generating EPR pairs in the
$\ket{\Psi}\coloneqq\nicefrac{{1}}{{\sqrt{2}}}(\ket{00}+\ket{11})$ state. In
our setting, the nodes have the ability to communicate classically and
quantumly, that is, they can send both purely classical messages, for the
header and trailer, and messages of quantum states which are noisy, for the
payload. Before the first EPR pair is generated, a classical header message is
sent across a channel. Following this, a payload worth of EPR pair halves is
sent across the channel. For a predefined payload size, once the size limit of
generated EPR pairs is reached, a termination trailer signal is sent signaling
the end of the frame.

The behaviour of the relay nodes is that they firstly await the classical
header message. Once it arrives, they pause for the maximum between the
duration of the processing time or the expected time for the total number of
qubits to arrive, while simultaneously qubits are arriving in the memory. Once
the processing delay elapses, the relay node firstly relays the classical
header message to the next hop and begins to send the qubits in the memory
onward. The qubits in the memory are emitted at the same rate they were
generated in the order they arrived. At the destination node, a header message
arrives followed by the qubits. The destination node in this case simply
measures (in a simulated way) the fidelity of the system. Fidelity is computed
using,

$\displaystyle
F\left(\rho\right)\coloneqq\left(\Tr\sqrt{\sqrt{\rho}\outerproduct{\Psi}{\Psi}\sqrt{\rho}}\right)^{2},$
(3)

where $\rho$ is the density matrix for a pair of entangled qubits at the time
of arrival.

The noise models used in the simulation are the following. For the
depolarizing noise model of the fiber we use the following model motivated by
[54, Eq. 18],

$\displaystyle p_{depol}(L,p_{L})=1-10^{-L\cdot p_{L}}.$ (4)

For the memory noise, we use the built-in `T1T2NoiseModel` NetSquid model
which is based on the memory properties with a $T_{1}$ relaxation time and a
$T_{2}$ dephasing time. This model is explained in detail [53, Eq. 1]. For
this simulation analysis, we ignore effects of loss, and only focus on the
noise. Future work will be to consider entanglement distribution rates where
each the channels are lossy. To coordinate the two parties in a lossy setting
would require a more complex protocol, where here we aim mainly to focus on
the depolarizing effects of the channel.

Figure 8: The network configurations used for simulating entanglement
distribution. In (a), there is a centralized node who generates pairs, sending
half of an EPR in one direction, and the other half in another direction. The
qubits are then routed through a linear chain of nodes. In (b), the entangled
pair is generated from one of the communicating parties, storing one half of
the pair in a memory, and emitting the other half through a linear chain of
nodes. Figure 9: An entanglement source with two spacial modes emits bipartite
entangled photons through two paths. Along the two paths, control information
for individual receivers is added to the individual signals and then sent into
the network for routing. Figure 10: The effect on fidelity with respect to the
number of hops in the line network. Here we fix $T_{1}=T_{2}=0.5$ ms and
processing time is set to $125\leavevmode\nobreak\ \mu$s. Qubits are emitted
from the source at a frequency of $5\leavevmode\nobreak\ \mu$s and
$p_{L}=0.008$. 10 qubits per frame, $5\leavevmode\nobreak\ \mu$s per pair.
Plot (a) is for the split transmission and plot (b) is for the sender source.

We begin with the analysis of the network configuration in Fig. 8 (a). In the
upper plot of Fig. 10, we see the fidelity of the entanglement with respect to
the total end-to-end distance of the two nodes sharing the entanglement, where
the distance ranges from $0$ km to $550$ km. The choice of parameters are
$T_{1}=T_{2}=0.5$ ms, pessimistically based on results from [36],
$p_{L}=0.008$ defined in (4) to approximately match experimental distances
[55], 10 qubits are sent per frame for good simulation performance, and an EPR
pair is generated every $5\leavevmode\nobreak\ \mu$s for the frame. The
header-processing delay is set to $125\leavevmode\nobreak\ \mu$s, a mid- to
higher-value based on control plane stability values in burst-switched
networks [56]. In the plots of Fig. 11 and Fig. 12, we show how the $T_{1}$
and $T_{2}$ times affect the entanglement fidelity within a network with 3
network hops during frame transmission. In Fig. 11, we use the same parameters
as above, except here we vary the $T_{1}$ and $T_{2}$ time and set
$T_{1}=T_{2}$. In Fig. 12, we vary the header processing time and use no
depolarizing noise in the fiber (i.e. $p_{L}=0)$.

We interpret the results as follows. For the upper plot in Fig. 10, we see, as
expected, a general worsening of entanglement fidelity with the increase in
total end-to-end length. As the entangled pairs enter more memories en route,
indeed the fidelity of the pairs diminishes. The rate of diminishment is the
smallest for a direct transmission of the pairs without any relays, where in
this case, the only depolarizing noise felt by the pairs is in the fiber. At
around $550$ km, in all cases the fidelity of the EPR pair falls to $0.5$,
rendering it unusable. In the cases with hops, indeed the $0.5$ fidelity mark
occurs at a shorter distance of roughly $400$ km. In the plot of Fig. 11, we
see that at roughly $10^{6}$ ns, or $1$ ms, is when the coherence times become
large enough that the fidelity begins to rapidly improve, indeed within the
next 1 or 2 orders of magnitude, the fidelity already converges to a maximum
for any given distance. We see, aligned with the previous results, eventually
the polarizing noise of the fiber becomes too strong with the distance and the
entanglement fidelity falls to 0.5 at around 500 km in the best cases. The
processing time effects are seen in Fig. 12. For small processing times in the
nanosecond scale, the requirements of the memory are relatively constant. With
microsecond storage times, varying of the processing time up to microsecond
scale plays no role on the fidelity of the entanglement. At a larger
processing times in the microsecond scale, we see that the processing time
begins to require larger demand of the memories, where memory times increase
directly proportionally to the increasing processing time.

Figure 11: A comparison of fidelity effects for varying $T_{1}=T_{2}$ and
length for distributing entanglement over three hops in a network. Here, the
data processing time is chosen as $125\leavevmode\nobreak\ \mu$s so that all
qubits arrive in a memory. The plot is for a centralized EPR source with a
split routing. Figure 12: A comparison of fidelity effects between the header
processing time and varying $T_{1}=T_{2}$ for network 3 hops. There are 20 kms
of fiber per hop, where three hops are used, and no fiber noise is used, that
is $p_{L}=0$. The plot is for a centralized EPR source with a split routing.

For the second scenario in Fig. 8 (b), we analyse the same settings. The
general trends follow the same patterns as in the previous network setting,
but here, the distance in which fidelity is maintained is about half as far.
In the lower plot of Fig. 10, the number of hops affects the fidelity
differently than in the case with a centralized source. Here only one part of
the entanglement travels across the fiber, and therefore only one part
experiences the depolarizing noise of the fiber. On the other hand, the other
part of the entanglement is stored in a memory for the entire duration of the
transmission, requiring a higher quality demand of the memory, and we see the
total end-to-end distance is halved in terms of usable EPR pairs with fidelity
above 0.5. The trends for the analogous plots for Fig. 11 and Fig. 12 are
excluded since for three hops, the trends vary only slightly. We plot the two
fidelity trends between the two cases in Fig. 13 in the simulation setting
used for Fig. 10. Indeed comparing hop-by-hop distance, the noise effects are
similar, and only the total lengths will vary in the plots. The single path
case performs better hop-by-hop in this parameter regime, but is limited to a
shorter distance since only one part of the entanglement travels.

Figure 13: Comparison between the two entanglement distribution settings. Here
we fix $T_{1}=T_{2}=0.5$ ms and processing time is set to
$125\leavevmode\nobreak\ \mu$s. Qubits are emitted from the source at a
frequency of $5\leavevmode\nobreak\ \mu$s and $p_{L}=0.008$. 10 qubits are
sent per frame and a rate of $5\leavevmode\nobreak\ \mu$s per pair.

##  V Integrating Packet-Switched Quantum Networks

The previous sections have been about packet switching at the link-layer
level. We defined a hybrid quantum Ethernet frame structure based on LLDP
frames and discussed switching approaches, analyzing some near-term
applications that can be deployed in this model. In order to scale quantum
networks up to the network-of-networks level, the best practices used in
conventional communication networks can offer much guidance. We therefore have
a good sense that for large scale general-purpose quantum inter-networks, the
higher network layers need to be adapted for scalability. Still though, in the
near-term, it is possible to stay at the link-layer level to support multiple
users at the metropolitan scale.

Indeed, proposals for quantum network stacks motivated by the Open Systems
Interconnection (OSI) model [57] have been proposed [16, 58] (also see [14]
for an in-depth comparison). These network stacks generally focus on robust
entanglement distribution, which is then used to perform quantum teleportation
as a means of quantum data transfer. Our design aims for a future network
where quantum and classical networks can be deployed over the same network
with a unified software and hardware stack. Finally, we describe a near-term
approach to overcoming scalability issues regarding network utilization and
communication distance in other quantum network models with an integrated
packet-switched approach.

###  V.1 Integration with Classical Optical Networks

In order to integrate our packet switching of hybrid frames approach within
current optical network switches, certain measures will need to be taken in
order merge the two signal types. Even in our near-term vision, changes to the
physical layer will need to be made to accommodate quantum signals being
transmitted over the same network as classical signals. Here we describe some
key issues that will need to be overcome when designing the first hybrid
classical-quantum network. To overcome these issues efficiently and robustly
will be the topic of future work.

Firstly, we will face the issue that quantum signals cannot be amplified. In
classical ROADM implementations, optical amplification is employed at both the
ingress and egress to compensate the loss of optical fiber and optical
components inside the ROADM [40]. Indeed removing this feature would not be an
option as it would be extremely detrimental to the classical communication
quality of service. Therefore methods for bypassing any optical amplifiers and
classical repeaters along the fiber and inside the switches will be required.

Next, if we aim to have quantum error correction ability as a feature of
hybrid switches, the geographical distance between switches will have to be
greatly reduced, or additional quantum repeater nodes will need to be
introduced between switches. To avoid any detrimental effects on the classical
communication signals, methods for bypassing the quantum repeaters along the
fiber or disable certain quantum functions inside the q-ROADM will also be
required.

Another major issue to overcome is the cross-talk when bright classical
signals and weak quantum signals coexist in the same fiber. Due to nonlinear
effects in optical fibers, noise photons generated by the strong classical
signals can greatly reduce the signal-to-noise ratio in the quantum channel
[59]. Ways to overcome this issue will require a combination of control-plane
scheduling and potentially using novel fiber technologies such as hollow-core
fiber. In hollow-core fiber, the nonliner effects are extremely small since
the signals are travelling through air rather than glass [20].

Finally, many state-of-the-art quantum technologies can only be operated in
carefully controlled environments, and it could be that switches capable of
processing both classical and quantum data will need to be put in a particular
container, sufficiently isolated from the environment to accommodate the
quantum hardware. In this regard, some photonics-based quantum technology can
already operate in room temperature [60], and research regarding extending the
capabilities of the technologies is a large field of research and commercial
interest [30, 61].

Overall, the path to completely integrated classical-quantum networks, where
both the control and data plane co-exist, is a long one, and many incremental
steps towards this goal will be needed. We envision that, although a full
integration of classical and quantum hardware at the physical layer is
unlikely, future networks could merge the hardware into a single device so to
support both data types and intelligently distinguish the processing path.

###  V.2 Integrating with Other Quantum Network Models

In Section III, we considered a near- and long-term versions of a quantum
ROADM. In the long-term vision, the ROADM is able to correct loss- and noise-
induced errors. In the short term, we consider a model only capable of storing
quantum states for relatively short times. What this implies is that the near-
term network model is not able to scale transmission to long distances. Indeed
with technologies such as low-loss hollow-core fiber, the distance may
potentially be extended [62], but still transmission to arbitrary distances is
not possible without a form of quantum repeater. What we will investigate here
is how our model of a packet-switched quantum network can be integrated with
the other proposals for quantum networks.

Figure 14: Two packet-switched networks are interconnected via an
entanglement-based teleportation channel. Quantum data from one network is
packet-switched to an egress of one subnetwork and is teleported to the
ingress of another via an entanglement-based network, using entanglement
swapping to establish end-to-end entanglement between the subnetwork edge
nodes.

For quantum networks with the purpose of QKD—also called QKD networks—the
integration with our model is straightforward. Current QKD networks based on
fiber connections generally use trusted nodes to extend the range of key
distribution. Secret keys are established point-to-point with the trusted node
and relayed over encrypted channels in a hop-by-hop fashion. In this case,
without quantum repeater technology, extending the range to arbitrary
distances is not possible without trusted nodes. Packet switching alone cannot
extend the range in this case, but we envision at metropolitan scale, with
packet switching, we can increase the network utilization and throughput. In
certain network traffic scenarios, low density traffic for one, packet
switching offers better network performance [63, 64]. A QKD network where the
nodes regenerate keys periodically, when using AES and reducing the need to
store large quantities of key material for example, is precisely this case, so
we believe improvements will be seen over current circuit-switched approaches.

A packet-switched quantum network integrated with an entanglement-based
network is how we envision near-term, general purpose quantum networks will
inter-network. What we envision is that at a metropolitan scale, a general-
purpose quantum network based on our packet-switched network model will act as
a sub-network, where first-generation quantum repeater chains capable of
performing entanglement swapping, would act as the backbone network, inter-
connecting multiple sub-networks via a “teleportation channel”. This
teleportation channel will have the sole purpose of generating long-distance
entanglement to teleport quantum states over distances exceeding the reach of
metropolitan scale, during the intermediate stage where quantum error
correction technology is in development. With this combination of network
types, we claim that scalability can be achieved in two directions—in the
number of network nodes and total distance. Depicted in Fig. 14 is the
described structure. Moreover, based on Section IV, packet-switched based
entanglement distribution can be used to implement the teleportation channel.

Using this structure, communication would work as follows: For intra-network
communication—communication contained to a subnet—the packet-switched approach
is used. When inter-network communication between distinct subnets is needed,
packet switching is used to move the quantum information to an egress of the
sub-network—a node connecting to the backbone entanglement-based network.
Teleportation is used to move the information to an ingress of the destination
subnet and then packet switching can again be used until the frame reaches the
final destination. By merging the two network types overcoming the
shortcomings of both approaches can be possible. Indeed to merge the two
network types will require interoperability between the hardware and so future
work will be to investigate this merger more concretely.

##  VI Conclusion and Discussion

In this work, we developed a novel packet switching paradigm for quantum
networks toward a quantum Internet that serves a large number of users. We
introduced three properties for quantum networks: Universality, Transparency,
and Scalability, on which we based our packet switching scheme. Our scheme is
aligned with the paradigms of modern networks, taking a step toward a packet-
switched quantum networks. We designed a classical-quantum hybrid data frame,
proposed switching approaches for near- and long-term, along with initial
hardware design ideas for processing and generating the frame, one of which a
quantum version of a ROADM. To the data frame structure, we added additional
properties in anticipation for quantum network technology capable of robustly
storing and error-correcting quantum information using the already established
LLDP frame structure. Next, we analyzed two quantum network use-cases suitable
for near-term use in our network model, showing proof-of-concept feasibility.
Lastly, we described how our model can integrate with other networks
describing various predicted hurdles.

Overall, in this work we have discussed a packet-switched quantum network up
to the link-layer. To increase the scale of such a network, we need to
continue up the network stack into the higher layers in order to fully
integrate network models towards global scale quantum networks. Moreover, the
control and data plane of the network will need a deep consideration in order
to integrate seamlessly with the current and coming network technologies. The
state of quantum networks is much like we have experienced with classical
networks, but precisely how future quantum networks will be deployed is yet to
be known. With this work, we propose changing the trend of deploying quantum-
only networks and instead to focus on how, with already established optical
technologies, large-scale quantum networks can be integrated to classical
networks, thereby unifying them.

## Acknowledgements

The authors thank Hassan Shapourian and Myungjin Lee for discussions during
the development of the manuscript.

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