We consider a star-shaped quantum network with a quantum switch in the center serving a number of requests, each characterized by two non-classical QoS requirements, the end-to-end entanglement delivery rate and the fidelity of the delivered entanglements. The central task of the switch is to allocate the limited entanglement resources among requests to maximize the system performance. We formulate the fundamental entanglement distribution problem where the switch decides 1) which requests to admit, and 2) as multiple requests may share a same quantum link, how to distributed the limited link-level entanglement resources among those competing requests. We then design a framework of joint entanglement purification scheduling and distribution for quantum switches. Our entanglement purification scheduling algorithm seeks to use minimal link-level entanglement resources to satisfy the QoS requirement of a single request. Our entanglement distribution algorithm further allocates the limited entanglement resources among multiple requests to maximize the overall utility by integrating the designed entanglement purification scheduling algorithm. We establish theoretical performance guarantee of our proposition, which is complemented by extensive numerical experiments demonstrating its effectiveness in a variety of network settings.
We consider a star-shaped quantum network with a quantum switch in the center serving a number of requests, each characterized by two non-classical QoS requirements, the end-to-end entanglement delivery rate and the fidelity of the delivered entanglements. The central task of the switch is to allocate the limited entanglement resources among requests to maximize the system performance. We formulate the fundamental entanglement distribution problem where the switch decides 1) which requests to admit, and 2) as multiple requests may share a same quantum link, how to distributed the limited link-level entanglement resources among those competing requests. We then design a framework of joint entanglement purification scheduling and distribution for quantum switches. Our entanglement purification scheduling algorithm seeks to use minimal link-level entanglement resources to satisfy the QoS requirement of a single request. Our entanglement distribution algorithm further allocates the limited entanglement resources among multiple requests to maximize the overall utility by integrating the designed entanglement purification scheduling algorithm. We establish theoretical performance guarantee of our proposition, which is complemented by extensive numerical experiments demonstrating its effectiveness in a variety of network settings.
Quantum switches are envisioned to be an integral component of future entanglement distribution networks. They can provide high quality entanglement distribution service to end-users by performing quantum operations such as entanglement swapping and entanglement purification. In this work, we characterize the capacity region of such a quantum switch under noisy channel transmissions and imperfect quantum operations. We express the capacity region as a function of the channel and network parameters (link and entanglement swap success probability), entanglement purification yield and application level parameters (target fidelity threshold). In particular, we provide necessary conditions to verify if a set of request rates belong to the capacity region of the switch. We use these conditions to find the maximum achievable end-to-end user entanglement generation throughput by solving a set of linear optimization problems. We develop a max-weight scheduling policy and prove that the policy stabilizes the switch for all feasible request arrival rates. As we develop scheduling policies, we also generate new results for computing the conditional yield distribution of different classes of purification protocols. The conclusions obtained in this work can yield useful guidelines for subsequent quantum switch designs.
Entanglement purification is a fundamental operation to combat against quantum decoherence and improve the fidelity of the entanglement. When multiple rounds of entanglement purification are performed, the fidelity of the final entanglement depends on the way how we schedule entanglement purification operations at each round. In this paper, we formulate and analyze the optimal entanglement purification scheduling problem arising from this context. Our main results include an optimal link-level purification scheduling algorithm and a joint entanglement purification scheduling and routing algorithm to establish fidelity-guaranteed end-to-end entanglements with quasi-optimal throughput in quantum networks. Our algorithmic framework developed in this paper can serve as functional building blocks for entanglement provisioning to support high-fidelity quantum information transfer by exploiting the limited quantum resources in a cost-effective way in order to fully realize the unrivalled capabilities offered by quantum networks.
Abstract Quantum networks can establish End-to-End (E2E) entanglement connections between two arbitrary nodes for various quantum applications through entanglement swapping. To support quantum applications reliably, quantum networks should establish E2E entanglement connections with desired entanglement fidelity by performing entanglement purification. The existing works provide mechanisms for link-level purification, which, however, leads to low throughput because of lacking consideration on purifications at network-level. (That is, efficiently allocating scarce resources to jointly purify entanglements under the situation with multiple concurrent requests in a network remains a critical but unsolved problem.) To address this problem, we analyze the cost of purification, design the E2E fidelity calculation method in detail, and propose a novel approach called Purification Scheduling Control (PSC). The basic idea of PSC is to determine the appropriate purification through jointly optimizing purification and resource allocation processes based on conflict avoidance. We conduct extensive experiments showing that PSC can maximize throughput under the fidelity requirement. This solution should spur the development of more applied reliable routing designs for quantum networks, combining quantum error correction, quantum applications, and computer network theory.
Quantum networks must deliver end-to-end entanglement whose fidelity meets application requirements, which typically requires entanglement purification along multi-hop paths. Existing scheduling approaches either purify at the link level or optimize end-to-end fidelity for a static set of requests, and do not capture concurrent requests competing for network resources over time. This paper studies concurrent entanglement purification scheduling in a time-slotted quantum network with heterogeneous links, in which requests compete for link capacity and quantum memories, and each request may be served by multiple parallel paths for increased reliability. We formulate a mixed-integer linear programming (MILP) scheduler that maximizes the number of scheduled requests, with max-min path allocation as a fairness criterion, and develop reinforcement learning (RL) schedulers based on DQN, PPO, and SAC, whose rewards balance request success against Bell-pair consumption. Simulations under varying network load, topologies and target fidelity thresholds show that the RL schedulers achieve the highest success rates, improving on MILP by up to 6% and on Progressive Filling and Greedy heuristics by 16.5% and 19.5% respectively, at the cost of higher Bell pair consumption and the deferral of a small fraction of requests. MILP, in contrast, achieves the highest fairness and the lowest Bell pair consumption in most scenarios.
Quantum networks, as a pivotal platform to support numerous quantum applications, have the potential to far exceed traditional communication networks. Establishing end-to-end entanglement connections with guaranteed fidelity is a key prerequisite for realizing the functionality of quantum networks. Entanglement purification techniques are commonly used in the entanglement distribution process to provide end-to-end entanglement connections that meet the fidelity requirements. Since the purification operation sacrifices a certain amount of entanglement resources, it is critical and challenging to efficiently utilize the scarce entanglement resources in quantum networks with concurrent competing requests. To address this problem, we propose a novel demand-oriented resource scheduling (DRS) algorithm. Considering the overall network demand, DRS introduces a congestion factor to evaluate the resource demand of each link, and performs purification operations sequentially based on the congestion level of the links, thus avoiding the excessive consumption of entanglement resources of bottleneck links. Extensive simulation results show that the DRS algorithm can achieve higher network throughput with similar resource conversion rates compared to traditional resource allocation schemes. Our work provides a new scheme for the resource scheduling problem under concurrent competing requests, which can promote the further development of existing entanglement routing techniques.
With a growing number of quantum networks in operation, there is a pressing need for performance analysis of quantum switching technologies. A quantum switch establishes, distributes, and maintains entanglements across a network. In contrast to a classical switching fabric, a quantum switch is a two-sided queueing network. The switch generates Link-Level Entanglements (LLEs) across links that connect users to the switch, which are then fused to process the network's entanglement requests. First, we characterize the capacity region that is defined as the set of entanglement request rates for which there exists a scheduling policy stabilizing the system. We then show that a sequence of Max-Weight policies that we propose achieve throughput optimality in the asymptotic sense. Our proof techniques analyse a two-time scale separation phenomenon at the fluid scale for a general switch topology. This allows us to demonstrate that the optimal fluid dynamics are given by a scheduling algorithm that solves a certain average reward Markov Decision Process.