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Entanglement Generation in Quantum Networks: Towards a universal and scalable quantum internet

Axel Dahlberg

Published Jan 6, 2021• 0 citations
Publisher

Abstract

Quantum mechanics shows that if one is able to generate and manipulate entanglement over a distance, one is able to perform certain tasks which are impossible using only classical communication. Classical communication refers to what is used in the Internet of today. A quantum internet would therefore bring new capabilities to our highly connected world. These capabilities both involve (1) the ability to perform tasks with are provably impossible in the current Internet, such as unconditionally secure communication, and (2) the ability to perform certain tasks much more efficient, such as distributed (quantum) computing or extending the baseline of telescopes. To be able to build a quantum internet, two main components are needed: (i) hardware that can store, manipulate and entangle qubits and (ii) a software stack to control the hardware. The core task of both of these is to generate entanglement to be used by applications. In this thesis we focus on the latter, i.e. the development of software and protocols that enable entanglement generation using capable hardware. To enable a certain application, one can certainly, in theory, manually specify each operation the hardware should perform, involving micro-wave pulses, lasers etc. However, in practice this is not feasible, if not to say impossible, due to the complexity of the operations needed, especially in a distributed system such as a quantum network. What is needed is a software stack, which can help with abstracting complexity away in multiple layers. This allows for someone to program a protocol in one layer without knowing all the details of the lower layers. In particular, one can abstract away the hardware details, in order to make higher-layer protocols and applications hardware-agnostic. Therefore, to be able to build a universal, efficient and scalable quantum internet, a software stack is crucial. In chapter 2 we start discussing the networking part of a software stack. Namely, we introduce a network stack for a quantum internet, drawing parallels to the IP/TCP-suite of the classical Internet. We continue with proposing a service and interface of the lowest layer of the network stack: the link layer. The link layer is here responsible for generating entanglement between nodes in a quantum network which are directly connected by a quantum link, i.e. a fiber cable. When developing a protocol or application it is very useful to be able to run it. Both to see if the intended ideas make sense and also to check that the implementation is actually correct. Currently we do not have quantum hardware that exposes a full-fledge API that can be used to execute applications. For this reason, it is very useful to be able to instead simulate the hardware in a way that exposes the same API as the hardware being developed. In chapter 3 we introduce SimulaQron for this exact purpose. Any application of a quantum internet will need entanglement in one way or another. However, entanglement is generally hard to generate and is usually the bottleneck when executing an application. We would therefore like to make use of the generated entanglement in the most optimal way. To be able to do this we need to understand how entanglement can be transformed and distributed in a quantum network. We study the entanglement of a particular class of states called graph states in chapters 4 to 9 and how these states can be transformed in a quantum network.

DOI
10.4233/uuid:f4ba6396-f4c0-4f8c-95be-2620d62e4387

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Quantum mechanics shows that if one is able to generate and manipulate entanglement over a distance, one is able to perform certain tasks which are impossible using only classical communication. Classical communication refers to what is used in the Internet of today. A quantum internet would therefore bring new capabilities to our highly connected world. These capabilities both involve (1) the ability to perform tasks with are provably impossible in the current Internet, such as unconditionally secure communication, and (2) the ability to perform certain tasks much more efficient, such as distributed (quantum) computing or extending the baseline of telescopes. To be able to build a quantum internet, two main components are needed: (i) hardware that can store, manipulate and entangle qubits and (ii) a software stack to control the hardware. The core task of both of these is to generate entanglement to be used by applications. In this thesis we focus on the latter, i.e. the development of software and protocols that enable entanglement generation using capable hardware. To enable a certain application, one can certainly, in theory, manually specify each operation the hardware should perform, involving micro-wave pulses, lasers etc. However, in practice this is not feasible, if not to say impossible, due to the complexity of the operations needed, especially in a distributed system such as a quantum network. What is needed is a software stack, which can help with abstracting complexity away in multiple layers. This allows for someone to program a protocol in one layer without knowing all the details of the lower layers. In particular, one can abstract away the hardware details, in order to make higher-layer protocols and applications hardware-agnostic. Therefore, to be able to build a universal, efficient and scalable quantum internet, a software stack is crucial. In chapter 2 we start discussing the networking part of a software stack. Namely, we introduce a network stack for a quantum internet, drawing parallels to the IP/TCP-suite of the classical Internet. We continue with proposing a service and interface of the lowest layer of the network stack: the link layer. The link layer is here responsible for generating entanglement between nodes in a quantum network which are directly connected by a quantum link, i.e. a fiber cable. When developing a protocol or application it is very useful to be able to run it. Both to see if the intended ideas make sense and also to check that the implementation is actually correct. Currently we do not have quantum hardware that exposes a full-fledge API that can be used to execute applications. For this reason, it is very useful to be able to instead simulate the hardware in a way that exposes the same API as the hardware being developed. In chapter 3 we introduce SimulaQron for this exact purpose. Any application of a quantum internet will need entanglement in one way or another. However, entanglement is generally hard to generate and is usually the bottleneck when executing an application. We would therefore like to make use of the generated entanglement in the most optimal way. To be able to do this we need to understand how entanglement can be transformed and distributed in a quantum network. We study the entanglement of a particular class of states called graph states in chapters 4 to 9 and how these states can be transformed in a quantum network.
The Internet has revolutionized the way we live. It has enabled applications far beyond what it was originally built for, and it will continue to exceed our expectations for the future. Quantum computers, and the network that will connect them—the Quantum Internet— are likely going to follow the same path. Differently from normal computers, quantum computers can share a property called entanglement, which allows the qubits (quantum bits) to be connected at a much more fundamental level. This property enables a range of new applications that span secure communication to enhanced metrology. Over the past fifteen years, significant progress has been made in connecting rudimentary quantum network nodes via long-distance entanglement. Several quantum platforms have demonstrated entanglement generation between two physically separated qubits. In this thesis we take a significant step forward, both in terms of experimental complexity achieved, and in the abstraction of said complexity for future developments. Moving past two-node experiments required a fundamental redesign of our experimental apparatus, as well as developing the capabilities to control simultaneously the additional node. The first result of this thesis is building a three-node entanglement-based quantum network. We demonstrated distribution of Greenberger-Horne-Zeilinger states over the network, as well as a building block for larger networks: entanglement swapping. Differently from previous multi-node demonstrations, which relied on post-selection, our network is able to perform the entanglement distribution in a heralded fashion: a signal will notify the users that the protocol was successful, and that the state is ready to be used. The second result builds on the first, by adding control over a fifth qubit, improving the quality of the entanglement, and introducing a novel repetitive readout technique, to achieve quantum teleportation of a qubit from the third node to the first—nodes that do not share a direct entanglement channel. The third and final result is the demonstration of entanglement delivery using a quantum network stack. The Internet is built using a plethora of physical platforms: optical fibers, Ethernet cables, Wi-Fi, satellite signals etc. To abstract their functionality, and make applications work regardless of the underlying platform, a layered approach was developed in the 1970s (the Internet protocol). Taking inspiration from classical network stacks, we demonstrate the first two layers of a quantum network stack, the physical layer (where the qubits, lasers and signal generators live), and the link layer, which abstracts the concepts of qubit and entanglement generation such that they can be used by applications at the higher-layers, hiding the complexity of the quantum platform being used.
Quantum communication brings radically new capabilities that are provably impossible to attain in any classical network. Here, we take the first step from a physics experiment to a fully fledged quantum internet system. We propose a functional allocation of a quantum network stack and construct the first physical and link layer protocols that turn ad-hoc physics experiments producing heralded entanglement between quantum processors into a well-defined and robust service. This lays the groundwork for designing and implementing scalable control and application protocols in platform-independent software. To design our protocol, we identify use cases, as well as fundamental and technological design considerations of quantum network hardware, illustrated by considering the state-of-the-art quantum processor platform available to us (Nitrogen-Vacancy (NV) centers in diamond). sing a purpose built discrete-event simulator for quantum networks, we examine the robustness and performance of our protocol using extensive simulations on a supercomputing cluster. We perform a full implementation of our protocol, where we successfully validate the physical simulation model against data gathered from the NV hardware. We first observe that our protocol is robust even in a regime of exaggerated losses of classical control messages with only little impact on the performance of the system. We proceed to study the performance of our protocols for 169 distinct simulation scenarios, including tradeoffs between traditional performance metrics such as throughput and the quality of entanglement. Finally, we initiate the study of quantum network scheduling strategies to optimize protocol performance for different use cases.
Quantum communication brings radically new capabilities that are provably impossible to attain in any classical network. Here, we take the first step from a physics experiment to a quantum internet system. We propose a functional allocation of a quantum network stack, and construct the first physical and link layer protocols that turn ad-hoc physics experiments producing heralded entanglement between quantum processors into a well-defined and robust service. This lays the groundwork for designing and implementing scalable control and application protocols in platform-independent software. To design our protocol, we identify use cases, as well as fundamental and technological design considerations of quantum network hardware, illustrated by considering the state-of-the-art quantum processor platform available to us (Nitrogen-Vacancy (NV) centers in diamond). Using a purpose built discrete-event simulator for quantum networks, we examine the robustness and performance of our protocol using extensive simulations on a supercomputing cluster. We perform a full implementation of our protocol in our simulator, where we successfully validate the physical simulation model against data gathered from the NV hardware. We first observe that our protocol is robust even in a regime of exaggerated losses of classical control messages with only little impact on the performance of the system. We proceed to study the performance of our protocols for 169 distinct simulation scenarios, including trade-offs between traditional performance metrics such as throughput, and the quality of entanglement. Finally, we initiate the study of quantum network scheduling strategies to optimize protocol performance for different use cases.
Building quantum networks ultimately requires strong use cases. As today's design and use of the Internet solely rests on the interconnection of classical computing devices, the development of hardware should take this dependence on an existing market into account. One might think quantum secure communication would be such a use case, but the entire design of the current Internet is built on the end-to-end argument and may reject the idea of implementing security as a physical layer protocol. On the other hand, higher data rates and reduced latency have been successfully used as key arguments for the conception of new communication standards. We thus argue that exactly these two figures of merit should be used again. We define two new initial stages of development of the quantum Internet, where in the first phase entanglement is only generated and used between network nodes, and in second phase entanglement swapping and thus distribution of entanglement over increasing distances becomes possible. In both phases, we show by simulation how the available new protocols increase the network capacity. Interestingly, following this envisioned approach can serve the needs of current market participants while paving the road for fully quantum applications in the future.
In a classical network the link layer is responsible for transferring a datagram between two nodes that are connected by a single link, possibly including switches. In a quantum network however, the link layer will need to provide a robust entanglement generation service between two quantum nodes which are connected by a quantum link. This service can be used by higher layers to produce entanglement between distant nodes or to perform other operations such as qubit transmission, without full knowledge of the underlying hardware and its parameters. This draft defines what can be expected from the service provided by a link layer for a Quantum Network and defines an interface between higher layers and the link layer.
The quantum internet is one of the frontiers of quantum information science. It will revolutionize the way we communicate and do other tasks, and it will allow for tasks that are not possible using the current, classical internet. The backbone of a quantum internet is entanglement distributed globally in order to allow for such novel applications to be performed over long distances. Experimental progress is currently being made to realize quantum networks on a small scale, but much theoretical work is still needed in order to understand how best to distribute entanglement and to guide the realization of large-scale quantum networks, and eventually the quantum internet, especially with the limitations of near-term quantum technologies. This work provides an initial step towards this goal. The main contribution of this thesis is a mathematical framework for entanglement distribution protocols in a quantum network, which allows for discovering optimal protocols using reinforcement learning. We start with a general development of quantum decision processes, which is the theoretical backdrop of reinforcement learning. Then, we define the general task of entanglement distribution in a quantum network, and we present ground- and satellite-based quantum network architectures that incorporate practical aspects of entanglement distribution. We combine the theory of decision processes and the practical quantum network architectures into an overall entanglement distribution protocol. We also define practical figures of merit to evaluate entanglement distribution protocols, which help to guide experimental implementations.