Optimal Switching Networks for Paired-Egress Bell State Analyzer Pools

To scale quantum computers to useful levels, we must build networks of quantum computational nodes that can share entanglement for use in distributed forms of quantum algorithms. In one proposed architecture, node-to-node entanglement is created when nodes emit photons entangled with stationary memories, with the photons routed through a switched interconnect to a shared pool of Bell state analyzers (BSAs). Designs that optimize switching circuits will reduce loss and crosstalk, raising entanglement rates and fidelity. We present optimal designs for switched interconnects constrained to planar layouts, appropriate for silicon waveguides and Mach-Zehnder interferometer (MZI) $2 \times 2$ switch points. The architectures for the optimal designs are scalable and algorithmically structured to pair any arbitrary inputs in a rearrangeable, non-blocking way. For pairing $N$ inputs, $N(N - 2)/4$ switches are required, which is less than half of number of switches required for full permutation switching networks. An efficient routing algorithm is also presented for each architecture. These designs can also be employed in reverse for entanglement generation using a shared pool of entangled paired photon sources.