A throughput optimal scheduling policy for a quantum switch

Abstract

We study a quantum switch that creates shared end-to-end entangled quantum states to multiple sets of users that are connected to it. Each user is connected to the switch via an optical link across which bipartite Bell-state entangled states are generated in each time-slot with certain probabilities, and the switch merges entanglements of links to create end-toend entanglements for users. One qubit of an entanglement of a link is stored at the switch and the other qubit of the entanglement is stored at the user corresponding to the link. Assuming that qubits of entanglements of links decipher after one time-slot, we characterize the capacity region, which is defined as the set of arrival rates of requests for end-to-end entanglements for which there exists a scheduling policy that stabilizes the switch. We propose a Max-Weight scheduling policy and show that it stabilizes the switch for all arrival rates that lie in the capacity region. We also provide numerical results to support our analysis.

A Continuous Variable Quantum Switch

“…The switch should make scheduling decisions to decide which requests to be processed using available elementary entanglements in such a way that requests are processed as quickly as possible. As in [7], the switch is considered to process requests in each time step based on a selected matching r = [r 1 , r 2 , ..., r k ] which indicates that the switch attempts to serve r i requests of type i by performing entanglement swapping operations. The term matching is defined as follows:…”

“…The above equation implies that the number of requested elementary entanglements as per the matching r, that are shared between user j and the switch should be at most one. We use the Max-Weight scheduling policy of [7] to make scheduling decisions at the switch that decides which matching should be selected from the set of all feasible matchings. We formally define the scheduling policy below:…”

“…In [7], the capacity region of a switch was found, defined as the set of request rates λ = [λ 1 , • • • , λ K ] for which there can exist a scheduling policy that stabilizes the switch, guaranteeing finite average waiting times for requests. If λ is not in the capacity region, then no scheduling policy can stabilize the switch.…”

“…in trapped ions [4] and color-centers in diamond [5]) and single photon polarization qubits. Quantum switches capable of routing mutliple DV quantum entanglement have also been studied [6], [7]. A switch typically operates in conjunction with repeater elements that help establish and store entanglement between the switch and the different nodes connected to its ports, followed by entanglement swapping across different sets of switch ports to support different entanglement flows.…”

“…A switch typically operates in conjunction with repeater elements that help establish and store entanglement between the switch and the different nodes connected to its ports, followed by entanglement swapping across different sets of switch ports to support different entanglement flows. It was proved recently that a Max-Weight scheduling policy is throughput optimal for a switch with quantum memories that have a lifetime of one time step that caters to several DV entanglement flows, where throughput optimality refers arXiv:submit/4499194 [quant-ph] 17 Sep 2022 to achieving stability of request queues associated with flows, for all feasible request rates [7].…”