QIRG                                                             C. Wang
Internet-Draft                                                 A. Rahman
Intended status: Informational          InterDigital Communications, LLC
Expires: July 26, 2021                                             R. Li
                                                              M. Aelmans
                                                        Juniper Networks
                                                        January 22, 2021

          Applications and Use Cases for the Quantum Internet


   The Quantum Internet has the potential to improve application
   functionality by incorporating quantum information technology into
   the infrastructure of the overall Internet.  This document provide an
   overview of some applications expected to be used on the Quantum
   Internet, and then categorize them using various classification
   schemes.  Some general requirements for the Quantum Internet are also
   discussed.  The intent of this document is to provide a common
   understanding, framework of applications and use cases for the
   Quantum Internet.

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   Copyright (c) 2021 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Conventions used in this document . . . . . . . . . . . . . .   3
   3.  Terms and Acronyms List . . . . . . . . . . . . . . . . . . .   3
   4.  Quantum Internet Applications . . . . . . . . . . . . . . . .   5
     4.1.  Overview  . . . . . . . . . . . . . . . . . . . . . . . .   5
     4.2.  Classification by Application Usage . . . . . . . . . . .   6
       4.2.1.  Quantum Cryptography Applications . . . . . . . . . .   6
       4.2.2.  Quantum Sensor Applications . . . . . . . . . . . . .   6
       4.2.3.  Quantum Computing Applications  . . . . . . . . . . .   7
     4.3.  Control vs Data Plane Classification  . . . . . . . . . .   7
   5.  Selected Quantum Internet Use Cases . . . . . . . . . . . . .   9
     5.1.  Secure Communication Setup  . . . . . . . . . . . . . . .   9
     5.2.  Secure Quantum Computing with Privacy Preservation  . . .  12
     5.3.  Distributed Quantum Computing . . . . . . . . . . . . . .  15
   6.  General Requirements  . . . . . . . . . . . . . . . . . . . .  17
     6.1.  Background  . . . . . . . . . . . . . . . . . . . . . . .  17
     6.2.  Requirements  . . . . . . . . . . . . . . . . . . . . . .  19
   7.  Conclusion  . . . . . . . . . . . . . . . . . . . . . . . . .  20
   8.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  20
   9.  Security Considerations . . . . . . . . . . . . . . . . . . .  21
   10. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . .  21
   11. Informative References  . . . . . . . . . . . . . . . . . . .  22
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  26

1.  Introduction

   The Classical Internet has been constantly growing since it first
   became commercially popular in the early 1990's.  It essentially
   consists of a large number of end-nodes (e.g., laptops, smart phones,
   network servers) connected by routers and clustered in Autonomous
   Systems.  The end-nodes may run applications that provide service for
   the end-users such as processing and transmission of voice, video or
   data.  The connections between the various nodes in the Internet
   include Digital Subscriber Lines (DSLs), fiber optics, coax cable and
   wireless that include Bluetooth, WiFi, cellular (e.g., 3G, 4G, 5G),

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   satellite, etc.  Bits are transmitted across the Classical Internet
   in packets.

   Research and experiments have picked up over the last few years for
   developing the Quantum Internet [Wehner].  It is anticipated that the
   Quantum Internet will provide intrinsic benefits such as improved
   end-to-end and network security.  End-nodes will also be part of the
   Quantum Internet, in that cased called quantum end-nodes that may be
   connected by quantum repeaters/routers.  These quantum end-nodes will
   also run value-added applications which will be discussed later.

   The connections between the various nodes in the Quantum Internet are
   expected to be primarily optical fiber and free-space optical.
   Photonic connections are particularly useful because light (photons)
   is very suitable for physically realizing qubits.  Unlike the
   Classical Internet, qubits (and not classical bits or packets) are
   expected to be transmitted across the Quantum Internet.  The Quantum
   Internet will operate according to unique physical principles such as
   quantum superposition and entanglement [I-D.irtf-qirg-principles].

   The Quantum Internet is not anticipated to replace, but more to
   enhance the Classical Internet.  For instance, quantum key
   distribution can improve the security of the Classical Internet; the
   powerful computation capability from quantum computing can expedite
   and optimize computation-intensive tasks (e.g., routing modelling) in
   the Classical Internet.  The Quantum Internet will run in conjunction
   with the Classical Internet to form a new Hybrid Internet.  The
   process of integrating the Quantum Internet with the Classical
   Internet is similar to, but with more profound implications, as the
   process of introducing any new communication and networking paradigm
   into the existing Internet.  The intent of this document is to
   provide a common understanding and framework of applications and use
   cases for the Quantum Internet.

2.  Conventions used in this document

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   document are to be interpreted as described in [RFC2119].

3.  Terms and Acronyms List

   This document assumes that the reader is familiar with the quantum
   information technology related terms and concepts that are described
   in [I-D.irtf-qirg-principles].  In addition, the following terms and
   acronyms are defined here for clarity:

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   o  Bit - Binary Digit (i.e., fundamental unit of information in a
      classical computer).

   o  Classical Internet - The existing, deployed Internet (circa 2020)
      where bits are transmitted in packets between nodes to convey
      information.  The Classical Internet supports applications which
      may be enhanced by the Quantum Internet.  For example, the end-to-
      end security of a Classical Internet application may be improved
      by secure communication setup using a quantum application.

   o  Fast Byzantine Negotiation - A Quantum-based method for fast
      agreement in Byzantine negotiations [Fitzi].

   o  Hybrid Internet - The "new" or evolved Internet to be formed due
      to a merger of the Classical Internet and the Quantum Internet.

   o  Local Operations and Classical Communication (LOCC) - A method
      where nodes communicate in rounds, in which (1) they can send any
      classical information to each other; (2) they can perform local
      quantum operations individually; and (3) the actions performed in
      each round can depend on the results from previous rounds.

   o  Noisy Intermediate-Scale Quantum (NISQ) - NISQ was defined in
      [Preskill] to represent a near-term era in quantum technology.
      According to this definition, NISQ computers have two salient
      features: (1) The size of NISQ computers range from 50 to a few
      hundred qubits (i.e., intermediate-scale); and (2) Qubits in NISQ
      computers have inherent errors and the control over them is
      imperfect (i.e., noisy).

   o  Packet - Formatted unit of multiple related bits.  The bits
      contained in a packet may be classical bits, or the measured state
      of qubits.

   o  Prepare-and-Measure - A set of Quantum Internet scenarios where
      quantum nodes only support simple quantum functionalities (i.e.,
      prepare qubits and measure qubits).  For example, BB84 [BB84] is a
      prepare-and-measure quantum key distribution protocol.

   o  Quantum End-node - An end-node hosts user applications and
      interfaces with the rest of the Internet.  Typically, an end-node
      may serve in a client, server, or peer-to-peer role as part of the
      application.  If the end-node is part of a Quantum Network (i.e,
      is a quantum end-node), it must be able to generate/transmit and
      receive/process qubits.  A quantum end-node must also be able to
      interface to the Classical Internet for control purposes and thus
      also be able to receive, process, and transmit classical bits/

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   o  Quantum Computer (QC) - A quantum end-node that also has quantum
      memory and quantum computing capabilities is regarded as a full-
      fledged quantum computer.

   o  Quantum Key Distribution (QKD) - A method that leverages quantum
      mechanics such as no-cloning theorem to securely distribute
      security keys from a sender to a receiver.

   o  Quantum Network - A new type of network enabled by quantum
      information technology where qubits are transmitted between nodes
      to convey information.  (Note: qubits must be sent individually
      and not in packets).  The Quantum Network will use both quantum
      channels, and classical channels provided by the Classical

   o  Quantum Internet - A network of Quantum Networks.  The Quantum
      Internet will be merged into the Classical Internet to form a new
      Hybrid Internet.  The Quantum Internet may either improve
      classical applications or may enable new quantum applications.

   o  Qubit - Quantum Bit (i.e., fundamental unit of information in a
      quantum computer).  It is similar to a classic bit in that the
      state of a qubit is either "0" or "1" after it is measured and is
      denoted as its basis state |0> or |1>.  However, the qubit is
      different than a classic bit in that the qubit can be in a linear
      combination of both states before it is measured and termed to be
      in superposition.  The Degrees of Freedom (DOF) of a photon (e.g.,
      polarization) or an electron (e.g., spin) can be used to encode a

4.  Quantum Internet Applications

4.1.  Overview

   The Quantum Internet is expected to be extremely beneficial for a
   subset of existing and new applications.  The expected applications
   using Quantum Internet are still being developed as we are in the
   formative stages of the Quantum Internet [Castelvecchi] [Wehner].
   However, an initial (and non-exhaustive) list of the applications to
   be supported on the Quantum Internet can be identified and classified
   using two different schemes.  Note, this document does not include
   quantum computing applications that are purely local to a given node
   (e.g., quantum random number generator).

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4.2.  Classification by Application Usage

   Applications may also be grouped by the usage that they serve into a
   tripartite classification.  Specifically, applications may be
   classified according to the following usages:

   o  Quantum cryptography applications - Refers to the use of quantum
      information technology to ensure secure communications (e.g.,

   o  Quantum sensors applications - Refers to the use of quantum
      information technology for supporting distributed sensors or
      Internet of Things (IoT) devices (e.g., clock synchronization).

   o  Quantum computing applications - Refers to the use of quantum
      information technology for supporting remote quantum computing
      facilities (e.g., distributed quantum computing).

   This scheme can be easily understood by both a technical and non-
   technical audience.  The next sections describe the scheme in more

4.2.1.  Quantum Cryptography Applications

   Examples of quantum cryptography applications include quantum-based
   secure communication setup and fast Byzantine negotiation.

   1.  Secure communication setup - Refers to secure cryptographic key
       distribution between two or more end-nodes.  The most well-known
       method is referred to as Quantum Key Distribution (QKD) [Renner],
       which have been mathematically proven to be unbreakable.

   2.  Fast Byzantine negotiation - Refers to a Quantum-based method for
       fast agreement in Byzantine negotiations [Fitzi], for example, to
       reduce the number of expected communication rounds and in turn
       achieve faster agreement, in contrast to classical Byzantine
       negotiations.  This can be used for improving consensus protocols
       such as practical Byzantine Fault Tolerance(pBFT), as well as
       other distributed computing features which use Byzantine

4.2.2.  Quantum Sensor Applications

   Example of quantum sensor applications include network clock
   synchronization, high sensitivity sensing, etc.  These applications
   mainly leverage a network of entangled quantum sensors (i.e. quantum
   sensor networks) for high-precision multi-parameter estimation

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   1.  Network clock synchronization - Refers to a world wide set of
       atomic clocks connected by the Quantum Internet to achieve an
       ultra precise clock signal [Komar] with fundamental precision
       limits set by quantum theory.

   2.  High sensitivity sensing - Refers to applications that leverage
       quantum phenomena to achieve reliable nanoscale sensing of
       physical magnitudes.  For example, [Guo] uses an entangled
       quantum network for measuring the average phase shift among
       multiple distributed nodes, to achieve high-sensitivity and
       distributed quantum sensing.

4.2.3.  Quantum Computing Applications

   Examples of quantum computing include distributed quantum computing
   and secure quantum computing with privacy preservation, which can
   enable new types of cloud computing.

   1.  Distributed quantum computing - Refers to a collection of remote
       small capacity quantum computers (i.e., each supporting a few
       qubits) that are connected and working together in a coordinated
       fashion so as to simulate a virtual large capacity quantum
       computer [Wehner].

   2.  Secure quantum computing with privacy preservation - Refers to
       private, or blind, quantum computation, which provides a way for
       a client to delegate a computation task to one or more remote
       quantum computers without disclosing the source data to be
       computed over [Fitzsimons].

4.3.  Control vs Data Plane Classification

   The majority of routers currently used in the Classical Internet
   separate control plane functionality and data plane functionality
   for, amongst other reasons, stability, capacity and security.  In
   order to classify applications for the Quantum Internet, a somewhat
   similar distinction can be made.  Specifically some applications can
   be classified as being responsible for initiating sessions and
   performing other control plane functionality.  Other applications
   carry application or user data and can be classified as data plane

   Some examples of what may be called control plane applications in the
   Classical Internet are Domain Name Server (DNS), Session Information
   Protocol (SIP), and Internet Control Message Protocol (ICMP).
   Furthermore, examples of data plane applications are E-mail, web
   browsing, and video streaming.  Note that some applications may
   require both control plane and data plane functionality.  For

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   example, a Voice over IP (VoIP) application may use SIP to set up the
   call and then transmit the VoIP user packets over the data plane to
   the other party.

   Similarly, nodes in the Quantum Internet applications may also use
   the classification paradigm of control plane functionality versus
   data plane functionality where:

   o  Control Plane - Network functions and processes that operate on
      (1) control bits/packets or qubits (e.g., to setup up end-user
      encryption); or (2) management bits/packets or qubits (e.g., to
      configure nodes).  For example, a quantum ping could be
      implemented as a control plane application to test and verify if
      there is a quantum connection between two quantum nodes.  Another
      example is quantum superdense coding (which is used to transmit
      two classical bits by sending only one qubit).  This approach does
      not need classical channels.  Quantum superdense coding can be
      leveraged to implement a secret sharing application to share
      secrets between two parties.  This secret sharing application
      based on quantum superdense encoding can be classified as control
      plane functionality.

   o  Data Plane - Network functions and processes that operate on end-
      user application bits/packets or qubits (e.g., voice, video,
      data).  Sometimes also referred to as the user plane.  For
      example, a data plane application can be video conferencing, which
      uses QKD-based secure communication setup (which is a control
      plane function) to share a secret key for encrypting and
      decrypting video frames.

   As shown in the table in Figure 1, control and data plane
   applications vary for different types of networks.  For a standalone
   Quantum Network (i.e., that is not integrated into the Internet),
   entangled qubits are its "data" and thus entanglement distribution
   can be regarded as its data plane application, while the signalling
   for controlling entanglement distribution be considered as control
   plane.  But looking at Quantum Internet, QKD-based secure
   communication setup, which may be based on and leverage entanglement
   distribution, is in fact a control plane application, while video
   conference using QKD-based secure communication setup is a data plane
   application.  In the future, two data planes may exist, respectively
   for Quantum Internet and Classical Internet, while one control plane
   can be leveraged for both Quantum Internet and Classical Internet.

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     |          |           |                |                      |
     |          | Classical |    Quantum     |      Hybrid          |
     |          | Internet  |    Internet    |      Internet        |
     |          | Examples  |    Examples    |      Examples        |
     |  Control | ICMP;     | Quantum ping;  | QKD-based secure     |
     |  Plane   | DNS       | Signalling for | communication        |
     |          |           | controlling    | setup                |
     |          |           | entanglement   |                      |
     |          |           | distribution;  |                      |
     |  Data    | Video     | QKD;           | Video conference     |
     |  Plane   | conference| Entanglement   | using QKD-based      |
     |          |           | distribution   | secure communication |
     |          |           |                | setup                |

        Figure 1: Examples of Control vs Data Plane Classification

5.  Selected Quantum Internet Use Cases

   The Quantum Internet will support a variety of applications and
   deployment configurations.  This section details a few key use cases
   which illustrates the benefits of the Quantum Internet.  In system
   engineering, a use case is typically made up of a set of possible
   sequences of interactions between nodes and users in a particular
   environment and related to a particular goal.  This will be the
   definition that we use in this section.

5.1.  Secure Communication Setup

   In this scenario, two banks (i.e., Bank #1 and Bank #2) need to have
   secure communications for transmitting important financial
   transaction records (see Figure 2).  For this purpose, they first
   need to securely exchange a classic secret cryptographic key (i.e., a
   sequence of classical bits), which is triggered by an end-user banker
   at Bank #1.  This results in a source quantum node A at Bank #1 to
   securely send a classic secret key to a destination quantum node B at
   Bank #2.  This is referred to as a secure communication setup.  Note
   that the quantum node A and B may be either a bare-bone quantum end-
   node or a full-fledged quantum computer.  This use case shows that
   the Quantum Internet can be leveraged to improve the security of
   Classical Internet applications of which the financial application
   shown in Figure 2 is an example.

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   One requirement for this secure communication setup process is that
   it should not be vulnerable to any classical or quantum computing
   attack.  This can be realized using QKD [ETSI-QKD-Interfaces].  QKD
   can securely establish a secret key between two quantum nodes,
   without physically transmitting it through the network and thus
   achieving the required security.  QKD is the most mature feature of
   the quantum information technology, and has been commercially
   deployed in small-scale and short-distance deployments.  More QKD use
   cases are described in ETSI documents [ETSI-QKD-UseCases].

   In general, QKD (e.g., [BB84]) without using entanglement works as

   1.  The source quantum node A transforms the secret key to qubits.
       Basically, for each classical bit in the secret key, the source
       quantum node A randomly selects one out of two bases and uses the
       selected basis to prepare/generate a qubit for the classical bit.

   2.  The source quantum node A sends qubits to the destination quantum
       node B via quantum channel.

   3.  The destination quantum node receives qubits and measures each of
       them in one of the two bases at random.

   4.  The destination quantum node informs the source node of its
       choice of basis for each qubit.

   5.  The source quantum node informs the destination node which random
       quantum basis is correct.

   6.  Both nodes discard any measurement bit under different quantum
       basis and remaining bits could be used as the secret key.  Before
       generating the final secret key, there is a post-processing.  For
       example, both nodes usually employ a part of the remaining bits
       to check if there were any errors and/or if there were an
       eavesdrop; another part of the remaining bits could be taken as
       the secret key.  Basically, if an eavesdropper tries to intercept
       and read qubits sent from node A to node B, the eavesdropper will
       be detected due to the no-cloning theorem of quantum mechanics.
       As a part of the post-processing, both nodes usually also perform
       information reconciliation [Elkouss] for efficient error
       correction and/or conduct privacy amplification [BTang] for
       generating the final information-theoretical secure keys.

   It is worth noting that:

   1.  There are some entanglement-based QKD protocols such as
       [Treiber], which work differently than above steps.  The

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       entanglement-based schemes, where entangled states are prepared
       externally to the source quantum node and the destination quantum
       node, are not normally considered "prepare-and-measure" as
       defined in [Wehner]; other entanglement-based schemes, where
       entanglement is generated within the source quantum node can
       still be considered "prepare-and-measure"; send-and-return
       schemes can still be "prepare-and-measure", if the information
       content, from which keys will be derived, is prepared within the
       source quantum node the source quantum node before being sent to
       the destination quantum node for measurement.

   2.  There are many enhanced QKD protocols based on [BB84].  For
       example, a series of loopholes have been identified due to the
       imperfections of measurement devices; there are several solutions
       to take into account these attacks such as measurement-device-
       independent QKD [PZhang].  These enhanced QKD protocol can work
       differently than the steps of BB84 protocol [BB84].

   3.  For large-scale QKD, QKD Networks (QKDN) are required, which can
       be regarded as a subset of a Quantum Internet.  A QKDN may
       consist of a QKD application layer, a QKD network layer, and a
       QKD link layer [Qin].  One or multiple trusted QKD relays
       [QZhang] may exist between the source quantum node A and the
       destination quantum node B, which are connected by a QKDN.
       Alternatively, a QKDN may rely on entanglement distribution and
       entanglement-based QKD protocols; as a result, quantum-repeaters/
       routers instead of trusted QKD relays are needed for large-scale

   4.  Although the addresses of Source Quantum Node A and Destination
       Quantum Node B could be identified and exposed, the identity of
       users, who will use the secret cryptographic key for secure
       communications, will not necessarily be exposed during QKD
       process.  In other words, there is no direct mapping from the
       addresses of quantum nodes to the user identity; as a result, QKD
       protocols do not disclose user identities.

   As a result, the Quantum Internet in Figure 2 contains quantum
   channels.  And in order to support secure communication setup
   especially in large-scale deployment, it also requires entanglement
   generation and entanglement distribution
   [I-D.van-meter-qirg-quantum-connection-setup], quantum repeaters/
   routers, and/or trusted QKD relays.

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        |   End User    |
        |(e.g., Banking |
        |  Application) |
              | User Interface
              | (e.g., GUI)
        +-----------------+     /--------\     +-----------------+
        |                 |--->( Quantum  )--->|                 |
        |     Source      |    ( Internet )    |  Destination    |
        |     Quantum     |     \--------/     |    Quantum      |
        |     Node A      |                    |     Node B      |
        | (e.g., Bank #1) |     /--------\     | (e.g., Bank #2) |
        |                 |    ( Classical)    |                 |
        |                 |<-->( Internet )<-->|                 |
        +-----------------+     \--------/     +-----------------+

                   Figure 2: Secure Communication Setup

5.2.  Secure Quantum Computing with Privacy Preservation

   Secure computation with privacy preservation refers to the following

   1.  A client node with source data delegates the computation of the
       source data to a remote computation node (i.e. a server).

   2.  Furthermore, the client node does not want to disclose any source
       data to the remote computation node and thus preserve the source
       data privacy.

   3.  Note that there is no assumption or guarantee that the remote
       computation node is a trusted entity from the source data privacy

   As an example illustrated in Figure 3, a terminal node such as a home
   gateway has collected lots of data and needs to perform computation
   on the data.  The terminal node could be a classical node without any
   quantum capability, a bare-bone quantum end-node or a full-fledged
   quantum computer.  The terminal node has insufficient computing power
   and needs to offload data computation to some remote nodes.  Although
   the terminal node can upload the data to the cloud to leverage cloud
   computing without introducing local computing overhead, to upload the
   data to the cloud can cause privacy concerns.  In this particular
   case, there is no privacy concern since the source data will not be

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   sent to the remote computation node which could be compromised.  Many
   protocols as described in [Fitzsimons] for delegated quantum
   computing or Blind Quantum Computation (BQC) can be leveraged to
   realize secure delegated computation and guarantee privacy
   preservation simultaneously.

   As a new client/server computation model, BQC generally enables: 1)
   The client delegates a computation function to the server; 2) The
   client does not send original qubits to the server, but send
   transformed qubits to the server; 3) The computation function is
   performed at the server on the transformed qubits to generate
   temporary result qubits, which could be quantum-circuit-based
   computation or measurement-based quantum computation.  The server
   sends the temporary result qubits to the client; 4) The client
   receives the temporary result qubits and transform them to the final
   result qubits.  During this process, the server can not figure out
   the original qubits from the transformed qubits.  Also, it will not
   take too much efforts on the client side to transform the original
   qubits to the transformed qubits, or transform the temporary result
   qubits to the final result qubits.  One of the very first BQC
   protocols such as [Childs] follows this process, although the client
   needs some basic quantum features such as quantum memory, qubit
   preparation and measurement, and qubit transmission.  Measurement-
   based quantum computation is out of the scope of this document and
   more details about it can be found in [Jozsa].

   It is worth noting that:

   1.  The BQC protocol in [Childs] is a circuit-based BQC model, where
       the client only performs simple quantum circuit for qubit
       transformation, while the server performs a sequence of quantum
       logic gates.  Qubits are transmitted back and forth between the
       client and the server.

   2.  Universal BQC in [Broadbent] is a measurement-based BQC model,
       which is based on measurement-based quantum computing leveraging
       entangled states.  The principle in UBQC is based on the fact the
       quantum teleportation plus a rotated Bell measurement realizes a
       quantum computation, which can be repeated multiple times to
       realize a sequence of quantum computation.  In this approach, the
       client first prepares transformed qubits and send them to the
       server and the server needs first to prepare entangled states
       from all received qubits.  Then, multiple interaction and
       measurement rounds happen between the client and the server.  For
       each round, the client computes and sends new measurement
       instructions or measurement adaptations to the server; then, the
       server performs the measurement according to the received
       measurement instructions to generate measurement results (qubits

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       or in classic bits); the client receives the measurement results
       and transform them to the final results.

   3.  A hybrid universal BQC is proposed in [XZhang], where the server
       performs both quantum circuits like [Childs] and quantum
       measurements like [Broadbent] to reduce the number of required
       entangled states in [Broadbent].  Also, the client is much
       simpler than the client in [Childs].  This hybrid BQC is a
       combination of circuit-based BQC model and measurement-based BQC

   4.  It will be ideal if the client in BQC is a purely classical
       client, which only needs to interact with the server using
       classical channel and communications.  [HHuang] demonstrates such
       an approach, where a classical client leverages two entangled
       servers to perform BQC, with the assumption that both servers can
       not communicate with each other; otherwise, the blindness or
       privacy of the client can not be guaranteed.  The scenario as
       demonstrated in [HHuang] is essentially an example of BQC with
       multiple servers.

   5.  How to verify that the server will perform what the client
       requests or expects is an important issue in many BQC protocols,
       referred to as verifiable BQC.  [Fitzsimons] discusses this issue
       and compares it in various BQC protocols.

   6.  Measurement-based quantum computation is out of the scope of this
       document.  [Jozsa] provides a good introduction of measurement-
       based quantum computation.

   In Figure 3, the Quantum Internet contains quantum channels and
   quantum repeaters/routers for long-distance qubits transmission

         +----------------+     /--------\     +----------------+
         |                |--->( Quantum  )--->|                |
         |                |    ( Internet )    |   Remote       |
         |   Terminal     |     \--------/     |   Computation  |
         |   Node         |                    |   Node         |
         |  (e.g., Home   |     /--------\     |   (e.g., QC    |
         |   Gateway)     |    ( Classical)    |   in Cloud)    |
         |                |<-->( Internet )<-->|                |
         +----------------+     \--------/     +----------------+

       Figure 3: Secure Quantum Computing with Privacy Preservation

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5.3.  Distributed Quantum Computing

   There can be two types of distributed quantum computing [Denchev]:

   1.  Leverage quantum mechanics to enhance classical distributed
       computing problems.  For example, entangled quantum states can be
       exploited to improve leader election in classical distributed
       computing, by simply measuring the entangled quantum states at
       each party (e.g., a node or a device) without introducing any
       classical communications among distributed parties [Pal].
       Normally, pre-shared entanglement needs first be established
       among distributed parties, followed by LOCC operations at each
       party.  And it generally does not need to transmit qubits among
       distributed parties.

   2.  Distribute quantum computing functions to distributed quantum
       computers.  A quantum computing task or function (e.g., quantum
       gates) is split and distributed to multiple physically separate
       quantum computers.  And it may or may not need to transmit qubits
       (either inputs or outputs) among those distributed quantum
       computers.  Pre-shared entangled states may be needed to transmit
       quantum states among distributed quantum computers without using
       quantum communications, similar to quantum teleportation.  For
       example, [Yimsiriwattana] has proved that a CNOT gate can be
       realized jointly by and distributed to multiple quantum
       computers.  The rest of this section focuses on this type of
       distributed quantum computing.

   As a scenario for the second type of distributed quantum computing,
   Noisy Intermediate-Scale Quantum (NISQ) computers distributed in
   different locations are available for sharing.  According to the
   definition in [Preskill], a NISQ computer can only realize a small
   number of qubits and has limited quantum error correction.  In order
   to gain higher computation power before fully-fledged quantum
   computers become available, NISQ computers can be connected via
   classic and quantum channels.  This scenario is referred to as
   distributed quantum computing [Caleffi] [Cacciapuoti01]
   [Cacciapuoti02].  This use case reflects the vastly increased
   computing power which quantum computers as a part of the Quantum
   Internet can bring, in contrast to classical computers in the
   Classical Internet, in the context of distributed quantum computing
   ecosystem [Cuomo].  According to [Cuomo], quantum teleportation
   enables a new communication paradigm, referred to as teledata
   [VanMeter01], which moves quantum states among qubits to distributed
   quantum computers.  In addition, distributed quantum computation also
   needs the capability of remotely performing quantum computation on
   qubits on distributed quantum computers, which can be enabled by the
   technique called telegate [VanMeter02].

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   As an example, scientists can leverage these connected NISQ computer
   to solve highly complex scientific computation problems such as
   analysis of chemical interactions for medical drug development [Cao]
   (see Figure 4).  In this case, qubits will be transmitted among
   connected quantum computers via quantum channels, while classic
   control messages will be transmitted among them via classical
   channels for coordination and control purpose.  Another example of
   distributed quantum computing is secure Multi-Party Quantum
   Computation (MPQC) [Crepeau], which can be regarded as a quantum
   version of classical secure Multi-Party Computing (MPC).  In secure
   MPQC, multiple participants jointly perform quantum computation on a
   set of input quantum states, which are prepared and provided by
   different participants.  One of primary aims of secure MPQC is to
   guarantee that each participant will not know input quantum states
   provided by other participants.  Secure MPQC relies on verifiable
   quantum secret sharing [Lipinska].

   For the example shown in Figure 4, qubits from one NISQ computer to
   another NISQ computer are very sensitive and should not be lost.  For
   this purpose, quantum teleportation can be leveraged to teleport
   sensitive data qubits from one quantum computer A to another quantum
   computer B.  Note that Figure 4 does not cover measurement-based
   distributed quantum computing, where quantum teleportation may not be
   required.  When quantum teleportation is employed, the following
   steps happen between A and B.  In fact, LOCC [Chitambar] operations
   are conducted at the quantum computer A and B in order to achieve
   quantum teleportation as illustrated in Figure 4.

   1.  The quantum computer A locally generates some sensitive data
       qubits to be teleported to the quantum computer B.

   2.  A shared entanglement is established between the quantum computer
       A and the quantum computer B (i.e., there are two entangled
       qubits: |q1> at A and |q2> at B).  For example, the quantum
       computer A can generate two entangled qubits (i.e., |q1>
       and |q2>) and sends |q2> to the quantum computer B via quantum

   3.  Then, the quantum computer A performs a Bell measurement of the
       entangled qubit |q1> and the sensitive data qubit.

   4.  The result from this Bell measurement will be encoded in two
       classical bits, which will be physically transmitted via a
       classical channel to the quantum computer B.

   5.  Based on the received two classical bits, the quantum computer B
       modifies the state of the entangled qubit |q2> in the way to

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       generate a new qubit identical to the sensitive data qubit at the
       quantum computer A.

   In Figure 4, the Quantum Internet contains quantum channels and
   quantum repeaters/routers [I-D.irtf-qirg-principles].  This use case
   needs to support entanglement generation and entanglement
   distribution (or quantum connection) setup
   [I-D.van-meter-qirg-quantum-connection-setup] in order to support
   quantum teleportation.

                           |     End-User    |
                           |(e.g., Scientist)|
                                    |User Interface (e.g. GUI)
                 |                                      |
                 |                                      |
                 V                                      V
         +----------------+     /--------\     +----------------+
         |                |--->( Quantum  )--->|                |
         |                |    ( Internet )    |                |
         |   Quantum      |     \--------/     |   Quantum      |
         |   Computer A   |                    |   Computer B   |
         | (e.g., Site #1)|     /--------\     | (e.g., Site #2)|
         |                |    ( Classical)    |                |
         |                |<-->( Internet )<-->|                |
         +----------------+     \--------/     +----------------+

                  Figure 4: Distributed Quantum Computing

6.  General Requirements

6.1.  Background

   Quantum technologies are steadily evolving and improving.  Therefore,
   it is hard to predict the timeline and future milestones of quantum
   technologies as pointed out in [Grumbling] for quantum computing.
   Currently, a NISQ computer can achieve fifty to hundreds of qubits
   with some given error rate.  In fact, the error rates of two-qubit
   quantum gates have decreased nearly in half every 1.5 years (for
   trapped ion gates) to 2 years (for superconducting gates).  The error
   rate also increases as the number of qubits increases.  For example,

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   a current 20-qubit machine has a total error rate which is close to
   the total error rate of a 7 year old two-qubit machine [Grumbling].

   On the network level, six stages of Quantum Internet development are
   described in [Wehner] as follows:

   1.  Trusted repeater networks (Stage-1)

   2.  Prepare and measure networks (Stage-2)

   3.  Entanglement distribution networks (Stage-3)

   4.  Quantum memory networks (Stage-4)

   5.  Fault-tolerant few qubit networks (Stage-5)

   6.  Quantum computing networks (Stage-6)

   The first stage are simple trusted repeater networks, while the final
   stage are quantum computing networks where the full-blown Quantum
   Internet will be achieved.  Each intermediate stage brings with it
   new functionality, new applications, and new characteristics.
   Figure 5 illustrates Quantum Internet use cases as described in this
   document mapped to the Quantum Internet stages described in [Wehner].
   For example, secure communication setup can be supported in Stage-1,
   Stage-2, or Stage-3, but with different QKD solutions.  More

   In Stage-1, basic and short-distance QKD is possible and can be
   leveraged to support secure communication setup but trusted nodes are
   required to provide end-to-end security.  The primary requirement is
   trusted nodes.

   In Stage-2, end-to-end security without relying on trusted nodes is
   possible to support secure communication setup too.  The primary
   requirement is long-distance qubit transmission to enable long-
   distance QKD.

   In Stage-3, end-to-end security can be enabled based on quantum
   repeaters and entanglement distribution, to support the same secure
   communication setup application.  The primary requirement is
   entanglement distribution to enable long-distance QKD.

   In Stage-4, Secure quantum computing with privacy-preservation can be
   enabled since it needs quantum memory for multiple rounds of quantum

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   Finally, in Stage-6, distributed quantum computing relaying more
   qubits can be supported.

     | Quantum |     Example Quantum       |                        |
     | Internet|      Internet Use         |   Characteristic       |
     | Stage   |         Cases             |                        |
     | Stage-1 | Secure Comm Setup         |  Trusted Nodes         |
     |         | with Basic QKD            |                        |
     | Stage-2 | Secure Comm Setup         |  Long-distance qubit   |
     |         | with Long-Distance QKD    |  transmission          |
     | Stage-3 | Secure Comm Setup         |  Entanglement          |
     |         | with Long-Distance QKD    |  distribution          |
     | Stage-4 | Secure/Blind Quantum      |  Quantum memory        |
     |         | Computing                 |                        |
     | Stage-5 | Higher-accuracy clock     |  Fault tolerance       |
     |         | synchronization           |                        |
     | Stage-6 | Distributed quantum       |  More qubits           |
     |         | computing                 |                        |

     Figure 5: Example Use Cases in Different Quantum Internet Stages

6.2.  Requirements

   Some general and functional requirements on the Quantum Internet from
   the networking perspective, based on the above applications and use
   cases, are identified as follows:

   1.  Methods for facilitating quantum applications to interact
       efficiently with entanglement qubits are necessary in order for
       them to trigger distribution of designated entangled qubits to
       potentially any other quantum node residing in the Quantum
       Internet.  To accomplish this specific operations must be
       performed on entangled qubits (e.g., entanglement swapping,
       entanglement distillation).  Quantum nodes may be quantum end-
       nodes, quantum repeaters/routers, and/or quantum computers.

   2.  Quantum repeaters/routers should support robust and efficient
       entanglement distribution in order to extend and establish

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       entanglement connection between two quantum nodes.  For achieving
       this, it is required to first generate an entangled pair on each
       hop of the path between these two nodes.

   3.  Quantum end-nodes must send additional information on classical
       channels to aid in transmission of qubits across quantum
       repeaters/receivers.  This is because qubits are transmitted
       individually and do not have any associated packet overhead which
       can help in transmission of the qubit.  Any extra information to
       aid in routing, identification, etc., of the qubit(s) must be
       sent via classical channels.

   4.  Methods for managing and controlling the Quantum Internet
       including quantum nodes and their quantum resources are
       necessary.  The resources of a quantum node may include quantum
       memory, quantum channels, qubits, established quantum
       connections, etc.  Such management methods can be used to monitor
       network status of the Quantum Internet, diagnose and identify
       potential issues (e.g. quantum connections), and configure
       quantum nodes with new actions and/or policies (e.g. to perform a
       new entanglement swapping operation).  New management information
       model for the Quantum Internet may need to be developed.

7.  Conclusion

   This document provides an overview of some expected applications for
   the Quantum Internet, and then details selected use cases.  The
   applications are first grouped by their usage which is a natural and
   easy to understand classification scheme.  The applications are then
   classified as either control plane or data plane functionality as
   typical for the classical Internet.  This set of applications may, of
   course, naturally expand over time as the Quantum Internet matures.
   Finally, some general requirements for the Quantum Internet are also

   This document can also serve as an introductory text to persons
   interested in learning about the practical uses of the Quantum
   Internet.  Finally, it is hoped that this document will help guide
   further research and development of the specific Quantum Internet
   functionality required to implement the applications and uses cases
   described herein.  To this end, a few key requirements for the
   Quantum Internet are specified.

8.  IANA Considerations

   This document requests no IANA actions.

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9.  Security Considerations

   This document does not define an architecture nor a specific protocol
   for the Quantum Internet.  It focuses instead on detailing use cases,
   requirements, and describing typical Quantum Internet applications.
   However, some useful observations can be made regarding security as

   It has been clearly identified that once large-scale quantum
   computing becomes reality it will be able to theoretically break many
   of the public-key (i.e., asymmetric) cryptosystems currently in use
   because of the exponential increase of computing power with quantum
   computing.  This would negatively affect many of the security
   mechanisms currently in use on the classic Internet.  This has given
   strong impetus for starting development of new cryptographic systems
   that are secure against quantum computing attacks [NISTIR8240].

   Paradoxically, development of the Quantum Internet will also mitigate
   the threats posed by quantum computing attacks against public-key
   cryptosystems.  Specifically, the secure communication setup feature
   of the Quantum Internet as described in Section 5.1 will be strongly
   resistant to both classical and quantum computing attacks against
   public-key cryptosystems.

   A key additional threat consideration for the Quantum Internet is
   pointed to by [RFC7258], which warns of the dangers of pervasive
   monitoring as a widespread attack on privacy.  Pervasive monitoring
   is defined as a widespread, and usually covert, surveillance through
   intrusive gathering of application content or protocol metadata such
   as headers.  This can be accomplished through active or passive
   wiretaps, traffic analysis, or subverting the cryptographic keys used
   to secure communications.

   Once again, the secure communication setup feature of the Quantum
   Internet as described in Section 5.1 will be strongly resistant to
   pervasive monitoring.  In addition, the intrinsic property of qubits
   to decohere if they are observed, albeit covertly, will allow
   detection of the pervasive monitoring if it somehow did occur.  In
   addition, Section 5.2 provides a method to perform remote quantum
   computing while preserving the privacy of the source data thus making
   it resistant to pervasive monitoring.

10.  Acknowledgments

   The authors want to thank Mathias Van Den Bossche, Xavier de Foy,
   Patrick Gelard, Alvaro Gomez Inesta, Wojciech Kozlowski, Rodney Van
   Meter, Joey Salazar, and Joseph Touch, and the rest of the QIRG

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   community as a whole for their very useful reviews and comments to
   the document.

11.  Informative References

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              Broadbent, A. and et. al., "Universal Blind Quantum
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              Cacciapuoti, A. and et. al., "Quantum Internet: Networking
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              Cacciapuoti, A. and et. al., "When Entanglement meets
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   [Childs]   Childs, A., "Secure Assisted Quantum Computation", 2005,

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              Chitambar, E. and et. al., "Everything You Always Wanted
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              Grumbling, E. and M. Horowitz, "Quantum Computing:
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   [RFC7258]  Farrell, S. and H. Tschofenig, "Pervasive Monitoring Is an
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   [Treiber]  Treiber, A. and et. al., "A Fully Automated Entanglement-
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Authors' Addresses

   Chonggang Wang
   InterDigital Communications, LLC
   1001 E Hector St
   Conshohocken  19428

   Email: Chonggang.Wang@InterDigital.com

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   Akbar Rahman
   InterDigital Communications, LLC
   1000 Sherbrooke Street West
   Montreal  H3A 3G4

   Email: rahmansakbar@yahoo.com

   Ruidong Li
   4-2-1 Nukui-Kitamachi
   Koganei, Tokyo  184-8795

   Email: lrd@nict.go.jp

   Melchior Aelmans
   Juniper Networks
   Boeing Avenue 240
   Schiphol-Rijk  1119 PZ
   The Netherlands

   Email: maelmans@juniper.net

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