The entanglement distribution process is widely en-visioned as one of the key functionalities of the Quantum Internet. Its engineering is, thus, foundational to effectively implement communication protocols in quantum networks. In this paper, we exploit the Markov Decision Process formalism to model the entanglement distribution as an optimal decision problem. Furthermore, we analyze the impact of reward functions on two key performance metrics, namely: the average distribution time and the average distributed cluster size. From this analysis, we gain some insights for choosing a reward function that meets suitable figures of merit for an overlaying communication protocol.
The entanglement distribution process is widely en-visioned as one of the key functionalities of the Quantum Internet. Its engineering is, thus, foundational to effectively implement communication protocols in quantum networks. In this paper, we exploit the Markov Decision Process formalism to model the entanglement distribution as an optimal decision problem. Furthermore, we analyze the impact of reward functions on two key performance metrics, namely: the average distribution time and the average distributed cluster size. From this analysis, we gain some insights for choosing a reward function that meets suitable figures of merit for an overlaying communication protocol.
Multipartite entanglement distribution is a key functionality of the Quantum Internet. However, quantum entanglement is very fragile, easily degraded by decoherence, which strictly constraints the time horizon within the distribution has to be completed. This, coupled with the quantum noise irremediably impinging on the channels utilized for entanglement distribution, may imply the need to attempt the distribution process multiple times before the targeted network nodes successfully share the desired entangled state. And there is no guarantee that this is accomplished within the time horizon dictated by the coherence times. As a consequence, in noisy scenarios requiring multiple distribution attempts, it may be convenient to stop the distribution process early. In this paper, we take steps in the direction of knowing when to stop the entanglement distribution by developing a theoretical framework, able to capture the quantum noise effects. Specifically, we first prove that the entanglement distribution process can be modeled as a Markov decision process. Then, we prove that the optimal decision policy exhibits attractive features, which we exploit to reduce the computational complexity. The developed framework provides quantum network designers with flexible tools to optimally engineer the design parameters of the entanglement distribution process.
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, especially with the limitations of near-term quantum technologies taken into account. This work provides an initial step toward this goal. In this work, we lay out a theory of near-term quantum networks based on Markov decision processes (MDPs), and we show that MDPs provide a precise and systematic mathematical framework to model protocols for near-term quantum networks that is agnostic to the specific implementation platform. We start by simplifying the MDP for elementary links introduced in prior work and by providing new results on policies for elementary links in the steady-state (infinite-time) limit. Then, we show how the elementary link MDP can be used to analyze a complete quantum network protocol. We then provide an extension of the MDP formalism to two elementary links. Here, as new results, we derive linear programing relaxations that allow us to obtain optimal steady-state policies with respect to the expected fidelity and waiting time of the end-to-end link.
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.
Superconducting and photonic technologies are envisioned to play a key role in the Quantum Internet. However the hybridization of these technologies requires functional quantum transducers for converting superconducting qubits, exploited in quantum computation, into ``flying'' qubits, able to propagate through the network (and vice-versa). In this paper, quantum transduction is theoretically investigated for a key functionality of the Quantum Internet, namely, multipartite entanglement distribution. Different communication models for quantum transduction are provided, in order to make the entanglement distribution possible. The proposed models departs from the large heterogeneity of hardware solutions available in literature, abstracting from the particulars of the specific solutions with a communication engineering perspective. Then, a performance analysis of the proposed models is conducted through key communication metrics, such as quantum capacity and entanglement generation probability. The analysis reveals that -- although the considered communication metrics depend on transduction hardware parameters for all the proposed models -- the particulars of the considered transduction paradigm play a relevant role in the overall entanglement distribution performance.
Distributing quantum entanglements over long distances is essential for the realization of a global scale quantum Internet. Most of the prior work and proposals assume an on-demand distribution of entanglements which may result in significant network resource under-utilization. In this work, we introduce Quantum Overlay Networks (QONs) for efficient entanglement distribution in quantum networks. When the demand to create end-to-end user entanglements is low, QONs can generate and store maximally entangled Bell pairs (EPR pairs) at specific overlay storage nodes of the network. Later, during peak demands, requests can be served by performing entanglement swaps either over a direct path from the network or over a path using the storage nodes. We solve the link entanglement and storage resource allocation problem in such a QON using a centralized optimization framework. We evaluate the performance of our proposed QON architecture over a wide number of network topologies under various settings using extensive simulation experiments. Our results demonstrate that QONs fare well by a factor of 40% with respect to meeting surge and changing demands compared to traditional non-overlay proposals. QONs also show significant improvement in terms of average entanglement request service delay over non-overlay approaches.
The vision of a global network that enables quantum communications between any point on Earth is known as the quantum internet. One crucial element of this network is the use of quantum repeater chains, which have the potential to overcome transmission losses and implement entanglement or quantum key distribution protocols over extended distances. There are various proposals for quantum repeaters, but they can generally be evaluated based on two main figures of merit: the average time for end-to-end entanglement delivery and the associated average fidelity. However, characterizing these quantities can be difficult due to factors such as feedback loops, decoherence, entanglement generation being a probabilistic process, and the potential failure of subprotocols. In this talk, I will discuss algorithmic and analytical methods for computing these quantities for relevant families of protocols.