Quantum simulation of partially distinguishable boson sampling

TL;DR

This paper introduces a quantum circuit that simulates boson sampling with particles of varying distinguishability, providing insights into how distinguishability causes decoherence and broadening the understanding of quantum sampling processes.

Contribution

A novel quantum circuit utilizing the quantum Schur transform to simulate partially distinguishable boson sampling, advancing the understanding of decoherence effects.

Findings

The circuit models the impact of distinguishability on boson sampling.

The approach offers a general framework applicable beyond boson sampling.

Provides a representation-theoretic perspective on particle distinguishability.

Abstract

Boson Sampling is the problem of sampling from the same output probability distribution as a collection of indistinguishable single photons input into a linear interferometer. It has been shown that, subject to certain computational complexity conjectures, in general the problem is difficult to solve classically, motivating optical experiments aimed at demonstrating quantum computational "supremacy". There are a number of challenges faced by such experiments, including the generation of indistinguishable single photons. We provide a quantum circuit that simulates bosonic sampling with arbitrarily distinguishable particles. This makes clear how distinguishabililty leads to decoherence in the standard quantum circuit model, allowing insight to be gained. At the heart of the circuit is the quantum Schur transform, which follows from a representation theoretic approach to the physics of distinguishable particles in first quantisation. The techniques are quite general and have application beyond boson sampling.