Strong simulation of tracking single photons with which-way-detectors in linear optics
Burhan Gülbahar · Quantum Science and Technology · 2022
Abstract Which-way-detectors (WWDs) are path-entangled detectors characterizing mutual exclusivity between path information and interference visibility in wave-particle duality experiments. We show surprisingly that WWDs allow to utilize single photons distinguishable in time domain to realize linear optical circuits where tracking their paths is exponentially hard for strong simulation analogous to rectangular lattice based Ising models. Distinguishable photons have scalability advantages of generation and detection compared with indistinguishable photons by promising both theoretical and experimental improvements in linear optical computing including boson sampling. We calculate strong simulation complexities by using variable elimination (VE) method for undirected graphs related to tensor network contraction for quantum circuits and recursive Feynman path-integral (RFPI) method to reduce space complexity. Two designs include either a single photon touring m times or m single photons propagating sequentially through an optical circuit composed of n beam splitters and phase shifters entangled with n WWDs. VE method for tracking results in undirected graphs matching with (2 m − 1) × (n + 1) and m × (n + 1) lattice Ising models with computational complexities of O ( m n 2 min ( 2 m − 1 , n + 1 ) ) and O ( m n 2 min ( m , n + 1 ) ) in time and O ( 2 m i n ( 2 m − 1 , n + 1 ) ) and O ( 2