Feynman path sum approach for simulation of linear optics

TL;DR

This paper introduces a Feynman path integral-inspired classical simulation method for linear optical boson sampling experiments, emphasizing efficiency and open-source implementation.

Contribution

It adapts the Feynman path integral formalism for simulating linear optics, providing a new, efficient classical algorithm and open-source code for boson sampling.

Findings

Efficient simulation of low-depth linear optical circuits.

Enhanced performance through tensor contraction techniques.

Open-source implementation available for community use.

Abstract

The Feynman path integral formalism has inspired the development of memory-efficient and parallelizable classical algorithms for simulating quantum computers. We adapt this approach for the calculation of probability amplitudes of linear-optical boson sampling experiments, which involve Fock-state inputs, linear optical circuits, and photo-detection at the output. We describe this simulation method and compare it with alternative approaches. Additionally, we implement a Linear-Optical Feynman Path simulator in open-source C code, enhancing its performance using tensor contraction techniques. Our method is benchmarked for low-depth linear optical circuits, where it offers advantages in runtime and memory efficiency.