Towards Large-Scale Quantum Networks

09/06/2019 ∙ by Wojciech Kozlowski, et al. ∙ Delft University of Technology 0

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

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1. Introduction

The objective of quantum networks is to fundamentally enhance communication technology by allowing the transmission and manipulation of quantum bits (qubits) between remote locations. Such networks will be embedded within classical networks as shown in Fig. 

1 and applications will have access to both quantum and classical channels. Quantum networks will be used to execute protocols that have no classical counterpart or are more efficient than what is possible classically. The range of possible quantum applications will depend on the development stage of the underlying hardware hardware (Wehner et al., 2018). This new networking paradigm has already opened up a range of new applications, which are provably impossible to realise using classical communication over the internet that we have today. Quantum key distribution (QKD) (Bennett and Brassard, 1984; Ekert, 1991) to ensure secure communication is the most famous example as it is also the only application that is ready for commercialisation and is undergoing standardisation. Whilst QKD will be the main focus for most near-term quantum networks, many other applications have already been put forward, with many more to be expected when such networks become widespread such as secure quantum computing in the cloud (Broadbent et al., 2009; Fitzsimons and Kashefi, 2017), clock synchronisation (Komar et al., 2014), and sensor networks (Giovannetti et al., 2004; Gottesman et al., 2012).

Figure 1. Quantum networks will be embedded within classical networks and use existing infrastructure to send and receive control messages. This can be achieved by adding a quantum data plane to existing networks. Note that the quantum and classical links do not have to coincide.

Quantum and classical networks.

Using features of quantum mechanics as the underlying physical mechanism for communication opens up many new possibilities, but also introduces considerable new design challenges. Some of these design challenges are due to fundamental differences between quantum and classical information, while others arise from technological limitations in engineering large-scale quantum systems. The first fundamental difference that quantum communication brings with it is the no-cloning theorem (Nielsen and Chuang, 2000). That is, arbitrary quantum data cannot be copied without destroying the original version. This means that it is impossible to use the same solutions that worked for classical networks which rely heavily on the ability to read and copy data for the purposes of retransmission and signal amplification. These limitations make transmitting qubits over long distances particularly challenging. The second fundamental difference arises due to a phenomenon called quantum entanglement. Entanglement is a special state of two or more qubits, that can in principle persist even if they are separated by arbitrary geographical distances and it is the key ingredient that enables long distance quantum communication. This property exists at the physical level and it requires that the location and state of its constituent qubits be known at all times. This is in contrast to classical communication, where signals at the physical layer typically proceed from the sender to the receiver and no state or notion of a connection exists. This introduces new demands for the control of such networks, as quantum data is inherently delocalised across multiple devices.

Design considerations that come from technological and not just fundamental limitations form an integral part of quantum network development and a key issue when considering realistic deployments. The technological challenges are immense, and include — for example — storing qubits for a long time or manipulating a large number of qubits simultaneously.

The remainder of this paper is structured as follows: Section 2 briefly surveys the current state of the art of quantum networked technologies and in Section 3 we give a basic introduction to the quantum physics of such networks. In Sections 4 and 5 we discuss the elements of a quantum network and a possible network stack respectively. Future research challenges are presented in Section 6 and the paper is concluded in 7.

2. State of the art

At present, no large-scale quantum networks exist. At short distances (~100 km in telecom fibre), devices that perform QKD are commercially available (Giovannetti et al., 2004; Inagaki et al., 2013; Diamanti et al., 2016; Extance, 2017). Early-stage demonstrations also achieve longer distances in the lab using coiled fibre (Boaron et al., 2018; Stucki et al., 2009; Hiskett et al., 2006; Minder et al., 2019; Zhong et al., 2019; Wang et al., 2019), or through free space communication (Schmitt-Manderbach et al., 2007; Vallone et al., 2015). QKD devices have been deployed in a variety of field tests and short-distance networks (Sasaki et al., 2011; Peev et al., 2009; Stucki et al., 2011; Wang et al., 2014).

While no long-distance quantum networks exist, short distance segments have been chained together classically to form so-called trusted repeater or trusted node networks (Salvail et al., 2010; Scarani et al., 2009). Such networks do not allow the end to end transmission of qubits, or the generation of entanglement and hence do not offer end-to-end security. They only enable secure communication between two end-points, provided that all the intermediate nodes are trusted. Such links of trusted nodes have been realised (Courtland, 2016; Sasaki et al., 2011), but require a high level of physical security to protect the trusted nodes. Such devices only produce short-lived (entanglement is not stored), short-distance entanglement and lack any of the features needed to bridge longer distances.

Long-range quantum communication, as well as the realisations of networks with functionalities more advanced than QKD, are presently still in their infancy. Entanglement between distant sites (~1200 km) has been produced using a satellite (Yin et al., 2017). However, data rates (~1 hz for 275 s per day) are still too low to produce a secret key, and the entanglement is short-lived. The present record for producing heralded entanglement between distant sites is 1.3 km in a solid state quantum device (nitrogen-vacancy (NV) centres in diamond) (Hensen et al., 2015). Longer distances have been observed for nodes in the same lab (Yu et al., 2019b). Demonstrations of more complex applications such as blind quantum computing (Barz et al., 2012) and quantum sensing (Guo et al., 2019) have also been realised in laboratory conditions.

Going forward, we would like to improve early-stage quantum communication in three directions. First, we would like to enable untrusted long-distance communication. Second, we would also like to enable the execution of more complex quantum network applications in order to take full advantage of our ability to transmit qubits. And finally, we would like to improve accessibility by allowing early stage access to such technology. The first realisation of such a network, a four-node demonstration in the Netherlands, is scheduled to be operational within the next 5–6 years. Much essential work is being done to build quantum hardware to make this possible, which is covered at length in the physics literature (Sangouard et al., 2011; Munro et al., 2015; Wehner et al., 2018).

3. Qubits and Entanglement

This subsection will briefly introduce the basic concepts of quantum computing and networking: qubits, quantum gates, and entanglement. For additional information see e.g. (Nielsen and Chuang, 2000).

3.1. Qubits

The differences between quantum computation and classical computation begin at the bit-level. A classical computer operates on the binary alphabet . Mathematically, a quantum bit, a qubit, exists over the same binary space, but unlike the classical bit, it can exist in a so-called superposition of the two possibilities:

(1)

where denotes a quantum state, here the binary and , and the coefficients and

are complex numbers called probability amplitudes satisfying

.

Upon measurement111In the standard basis, given by , the qubit loses its superposition and irreversibly collapses into one of the two basis states, either or , and yields the corresponding value, or , as the measurement readout. The outcome of the measurement is not deterministic, and the probability of measuring and collapsing the state to is and similarly the probability of measuring and collapsing the state to is . This randomness is not due to our ignorance of the underlying mechanisms, but rather it is a fundamental feature of a quantum mechanical system.

Many possible realisations of qubits exists. Key to all these representations, is to find a realisation of the classical states and , together with a procedure to create arbitrary superpositions thereof. For quantum memories, and quantum computing devices, and typically correspond to states of two different energies in either a natural “atomic system” (e.g. ion traps (Häffner et al., 2008), NV centres in diamond (Togan et al., 2010), neutral atoms (Briegel et al., 2000) or atomic ensembles (Sangouard et al., 2011)), or artificially designed nano-scale systems (e.g. superconducting quantum processors (Clarke and Wilhelm, 2008)). For transmission, usually optically, qubits can be represented in a variety of ways: the two states and can be encoded in the presence or absence of a photon (Humphreys et al., 2018; Cabrillo et al., 1999), a time-bin encoding of early and late arrival (Brendel et al., 1999), or the horizontal and vertical polarisation of photons (Bennett and Brassard, 1984; Mattle et al., 1996).

3.2. Multiple Qubits

We can express the state of an -qubit quantum state as

(2)

where . We remark that this means that since there are possible strings , we need an exponential number of parameters in order to describe the definite state . This is in sharp contrast to classical computing, where only parameters are needed (namely a specific string ).

As an example, if we have two qubits and , and the first qubit is in a state and the second in a state , then the overall state of the two qubits can be expressed as . However, there exists multi-qubit states which cannot be written as such a combination of single qubit states. That is, the two qubits can non longer be described independently of each other. The states of the two individual qubits are now correlated beyond what is possible to achieve classically. Such states are called entangled. For two-qubits the maximally entangled state can (up to local quantum gates) be written as

(3)

Such states have an interesting property that for any measurement on that probabilistically yields outcome , there always exists a measurement on that yields exactly the same outcome . Very intuitively, such states can hence be understood as the quantum analogue of maximal correlation in the classical domain, only such correlations persist for any measurement. Entanglement enables much stronger than classical correlations, also for more complex scenarios (Van Meter, 2014). Interestingly, entanglement cannot be shared, which is also known as the monogamy of entanglement (Terhal, 2004).

An entangled state is created from initially unentangled qubits, say . A common scheme to locally create an entangled state is to start by applying the so-called Hadamard operation on to produce . Subsequently a controlled NOT operation (CNOT) is performed which has the effect :

(4)

The physical implementation depends on the underlying hardware platform. For NV centres in diamond this operation can be implemented using a combination of a microwave and optical pulses (Hensen et al., 2015).

3.3. Teleportation

Qubits may be transmitted directly, or via quantum teleportation (Bennett et al., 1993) using entanglement. To teleport one data qubit , we require one entangled pair to be established between the sender and receiver ahead of time. The sender performs a measurement of the data qubit and their qubit of (see Fig. 2), resulting in two classical bits as the measurement outcome. The sender transmits to the receiver, who applies a correction depending on on their qubit in order to recover . From the perspective of control of such a network, we remark that this requires that the sender has correctly identified that qubit belongs to the entangled state shared with the receiver, and that the entanglement is consumed by this process. Deterministic teleportation has been realised, using for example two network nodes based on NV in diamond (Pfaff et al., 2014).

Teleportation is crucial for quantum networking. The no-cloning theorem means that retransmitting the data qubit if sending fails is not an option. However, is a known generic state that does not carry any data and can be repeatedly recreated until it has been successfully distributed to the sender and receiver. At this point the sender simply teleports the sensitive data qubit to the receiver without putting it through the network risking its loss.

Figure 2. Entangled Bell pairs enable long-distance quantum communication. (a) An unknown data qubit state can be teleported over long distances by consuming a Bell pair that has one qubit at the source and the other qubit at the destination. (b) Two shorter Bell pairs can be combined into a longer Bell pair with an entanglement swap operation.

Quantum teleportation and entanglement swapping.

3.4. Entanglement Swapping

Teleportation also provides a mechanism to extend short-distance entanglement to larger distances (Munro et al., 2015; Briegel et al., 1998; Dür et al., 1999). Consider node which has generated entanglement with node . Similarly, has produced entanglement with . We can now generate entanglement between and using the help of : teleports the qubit entangled with node to , using the entanglement he shares with . This process is also known as entanglement swapping (Briegel et al., 1998; Zukowski et al., 1993) (see Fig. 2).

Unfortunately, neither the entanglement generation nor the swapping operations are noiseless. Therefore, with each link and each swap the quality of the entanglement, called fidelity, degrades. However, it is possible to create higher fidelity entangled pairs from two or more lower quality pair states through a process called distillation using the Purify-and-Swap algorithm (Briegel et al., 1998). Therefore, once the quality loss over a given distance become prohibitive, additional redundancy may be used to restore the state fidelity.

4. Elements of a Quantum Network

Let us provide a high-level overview of the elements of a quantum network (Wehner et al., 2018). For additional overview of design considerations for quantum networks we also refer to Refs. (Dahlberg et al., 2019; Van Meter, 2014; Van Meter and Touch, 2013).

End Nodes:

Just like in classical networks we need devices at the edge of the network on which applications are run. In the simplest case, these are photonic devices consisting of linear optical elements, photon sources and detectors. These do not have a quantum memory to store qubits, and can also only perform a limited set of quantum operations deterministically. However, these are sufficient to perform all protocols in the prepare and measure stage of quantum network (Wehner et al., 2018) at short distances (presently ~100 km over deployed telecom fibre), such as QKD.

However, they may also be processing nodes with an optical interface which are capable of storing qubits, as well as performing universal quantum computation. Examples include NV centres in diamond (Hensen et al., 2015; Bernien et al., 2013; Taminiau et al., 2014), ion traps (Moehring et al., 2007), and neutral atoms (Reiserer and Rempe, 2015). Such systems can also be used to run application protocols in the quantum memory network stage and eventually above (Wehner et al., 2018).

Quantum repeaters:

The objective of quantum repeaters is to transmit qubits over long-distances. Any system that is a quantum processing node, can also be used as a repeater platform. In addition, there exist specific hardware platforms tailored to the task of a quantum repeater. This includes multiplexed quantum repeaters (Sangouard et al., 2011) which promise to generate entanglement quickly by temporal and spatial multiplexing. These repeater platforms work — in a possible combination with entanglement distillation steps — by the entanglement swapping principle outlined in Fig. 2. Theoretical proposals for employing forward error correction also exist (Muralidharan et al., 2014), but they are not possible to realise in the near-term.

The current world record for producing such heralded (i.e. confirmed) entanglement is 1.3 km which has been achieved using NV centres in diamond (Hensen et al., 2015), see Fig. 3. This platform is a few (about 10 (Bradley et al., 2019)) qubit quantum computer with an optical interface capable of executing arbitrary gates and measurements. It has been recently demonstrated that NV centres are capable of memory lifetimes approaching one minute (Bradley et al., 2019) in nodes not yet interfaced to the network. Other platforms exist that are similar on the conceptual level with similar capabilities such as ion traps (Inlek et al., 2017) and neutral atoms (Reiserer and Rempe, 2015) (see Table 1 for current parameter trade-offs).

Figure 3. Example of a physical implementation producing entanglement between two quantum processors (NV in diamond). (a) The qubits of the Bell pair are stored in NV centres in diamond on (b) custom chips. (c) Entanglement is generated between the two processors using probabilistic entanglement swapping: entanglement is produced between each processor and a traveling qubit (photon) sent to the mid-point. The mid-point performs entanglement swapping, and sends a confirmation (heralding) signal back to the nodes whether entanglement generation was a success.

Quantum link experimental setup.

Communication lines:

Qubits can be sent using photons through fibre, or free space communication (Yu et al., 2019b). Standard telecom fibre can be used for this purpose, potentially following an appropriate wavelength conversion to the telecom band (Dréau et al., 2018; Zaske et al., 2012).

Platform QLE
NV Centres (Humphreys et al., 2018)
Trapped Ions (Hucul et al., 2015)
Neutral Atoms 2 (projected) (Nölleke et al., 2013; Körber et al., 2018)
Table 1. Quantum Link Efficiency (QLE) is given by the ratio of the entangling rate to the decoherence rate, capturing how fast entanglement can be produced in relation to how fast it is lost. A QLE is required to extend entanglement over long distances.

Classical Control Messages

A crucial component of quantum communication is also the ability to send classical data. The control of quantum devices requires quite a number of classical control signals to be exchange, teleportation being just one example. In order to develop functional quantum protocols we will need a way to transmit control information between the quantum repeaters. This means that it is expected that quantum networks will be deployed alongside classical networks with a quantum data plane coexisting with the classical one as shown in Fig. 1.

5. A Quantum Network Stack

One may wonder whether one can design quantum network protocols without detailed knowledge of the underlying hardware system. Here, we briefly summarise the approach of Ref. (Dahlberg et al., 2019), because it is defined in terms of service layers rather than protocol layers (see Fig. 4) which gives it a structure that is similar to the classical TCP/IP stack. It also gives a concrete link layer protocol that abstracts away from the underlying hardware system, turning entanglement generation into a well-defined service.

Figure 4. Functional allocation in a quantum network stack. The structure mirrors and is inspired by the classical TCP/IP network stack.

Quantum network stack.

Physical

This layer corresponds to the actual quantum hardware devices and physical connections. The physical layer keeps no state related to entanglement production, produced entanglement probabilistically, and has no decision making capabilities. The hardware is solely responsible for tasks such as time synchronisation, photon emission, laser phase stabilisation, and so on, that are required to actually produce entangled Bell pairs.

Link

The task of the link-layer is to utilise the physical layer’s ability to produce entanglement between neighbouring nodes reliably. It also integrates the quantum and classical data planes providing sufficient information for higher level protocols and network management. A concrete link layer protocol can be found in (Dahlberg et al., 2019).

Network

Similar to a network layer in classical networking, the task of the network layer is to enable the generation of entanglement between network nodes which are not directly connected. A protocol to achieve this would utilise the link layer to produce entanglement between neighbouring nodes followed by entanglement swaps to create long distance links.

Transport

One can imagine, that a transport layer could provide the additional service of transmitting qubits to the application layer. This could be realised by, for example, pre-generating entangled pairs of qubits using the network layer, followed by teleportation to ensure reliable end-to-end delivery of qubits.

6. Challenges and Requirements

Quantum networks are still in their early infancy. Realising the necessary quantum hardware is of paramount importance and presents many challenges, but that is only one part of the story. Here, we present some of the challenges beyond hardware accounting for the fundamental differences inherent to quantum communication and mitigating the limitations and imperfections at the physical level. Further design considerations can also be found in (Dahlberg et al., 2019).

Timely decision making

Quantum memory lifetimes are extremely short even in the most sophisticated setups and this directly impacts our ability to produce long-distance entanglement by means of entanglement swapping. Entanglement swapping requires that both entangled pairs of qubits are available on two separate links at the same time so the intermediate node must be able to store the first pair until it receives the second pair. If one of the qubits decoheres, the pair is lost and the entire process must start over. One approach to increase the likelihood of such a coincidence event lies in proposals to perform massive multiplexing (Sangouard et al., 2011) significantly reducing the required storage time. There is also the obvious approach of increasing memory lifetime. NV centres in diamond already exhibit a high QLE, see Table 1, and lifetimes up to a minute have recently been observed in NV nodes not yet connected to a network (Bradley et al., 2019). Longer memory lifetimes impose less stringent demands on timing at the network layer allowing it to be kept at the physical layer.

Nevertheless, mitigating limited qubit lifetimes is essential and demands fast and reactive control of the network. In a network based on entanglement swapping it also raises the interesting question of whether such entanglement is produced only on-demand, or if there exists a mechanism which continuously generates entangled pairs at all times between certain links of the network.

Extending the network stack

In parallel with the effort of building the physical network links there is a need for work to build up the quantum network stack vertically. The first link-layer protocol has been proposed (Dahlberg et al., 2019). However, to go beyond point-to-point connectivity between two directly connected nodes we need a network layer service and the transport layer to provide platform-independent services for distributed quantum applications. The first end-to-end quantum communication protocols have started to appear though they generally assume hardware capabilities beyond what is possible in the near-term future (Matsuo et al., 2019; Yu et al., 2019a).

Routing

In addition to forwarding protocols necessary to actually generate an end-to-end Bell pair there are many other second-level mechanisms necessary for a fully functional quantum internet. The specific question of routing entanglement, i.e. making decisions on how end-to-end entanglement can be established quickly between users in future quantum networks, is seeing more attention (Caleffi, 2017; Gyongyosi and Imre, 2018; Van Meter et al., 2013; Schoute et al., 2016; Gyongyosi and Imre, 2017; Pant et al., 2019). Routing in quantum networks is a non-trivial problem due to the non-local and temporary nature of entangled pairs as well as different physical resource requirements necessary for delivering these pairs with a high enough fidelity.

SDN Integration

Given limited lifetimes, building robust and efficient quantum network routing and management protocols in an entirely distributed manner may be difficult. This could make software-defined networking (SDN) a very attractive direction for quantum networking and has already been considered for QKD (Ou et al., 2018).

SDN is an architecture for programmable networks that splits the vertical integration of the forwarding and control planes and puts much of the decision-making capabilities in a centralised controller (physically decentralised with appropriate redundancy) (Kreutz et al., 2015). In this approach, the central controller has network-wide visibility and it is responsible for most (or all as is the case for OpenFlow) control plane decisions based on input it receives from the individual nodes in the network. It is plausible that in a quantum network a controller would be responsible for managing the global strategies for the distribution of long-distance Bell pairs (Bell pairs that have been produced as a result of entanglement swaps between separate links), but connection establishment, Bell pair generation, and other localised operations are left to the actual devices who will try to conform to the controller’s strategy.

Security

Given that one of the most important features quantum networking brings with it is enhanced security it is crucial that a design for a future quantum network architecture incorporates strong security features itself. Such design considerations should be employed already at the physical layer, to ensure the protection of quantum network nodes. For example, we remark that convincing a remote node to produce entanglement with its neighbour may simply lead to a denial of service attack consuming its resources (Dahlberg et al., 2019). This shows that at the very least authentication is necessary for control messages already at the physical layer. Such authentication could be realised using standard classical mechanisms, or also use keys generated by QKD in combination with an information-theoretically secure authentication scheme.

7. Conclusion

There is a tremendous amount of work to do to build a fully functional quantum network, both at the physical level and at the systems and software level. Recent experimental progress in entanglement generation rates and memory lifetimes is very promising and the breadth of the combined research effort should result in practical demonstrations very soon. Nevertheless, there are a lot of open questions and research challenges that are unresolved and require a range of expertise from beyond physics such as operating systems, computer networks, and communications. This opens up many new opportunities for researchers from outside the usual circles to contribute to the growing field of quantum networking.

Acknowledgements

The authors of this memo acknowledge funding received the EU Flagship on Quantum Technologies, Quantum Internet Alliance, an ERC Starting Grant (SW) and an NWO VIDI Grant (SW). The authors would further like to thank (Dahlberg et al., 2019) for permission to reuse some of their figures.

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