Applications and Use Cases for the Quantum Internet

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).¶

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:¶

• Quantum cryptography applications - Refers to the use of quantum information technology to ensure secure communications (e.g., QKD).¶
• 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).¶
• 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 detail.¶

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 functionality.¶

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 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:¶

• 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.¶
• 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.¶

+----------+-----------+----------------+----------------------+
|          |           |                |                      |
|          | 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                |
+--------------------------------------------------------------+

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.¶

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 follows:¶

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 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 QKD.¶
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.¶

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

5.2. Secure Quantum Computing with Privacy Preservation

Secure computation with privacy preservation refers to the following scenario:¶

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 perspective.¶

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 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 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 model.¶
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 [I-D.irtf-qirg-principles].¶

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

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].¶

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 communications.¶
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 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 )<-->|                |
+----------------+     \--------/     +----------------+

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, 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 specifically:¶

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 computation.¶

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                 |                        |
+--------------------------------------------------------------+

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 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.¶