The scaling of boson sampling experiments

TL;DR

This paper derives scaling laws for boson sampling experiments using random matrix theory, demonstrating that nonclassical behavior can be verified at large scales despite losses.

Contribution

It introduces a theoretical framework to predict how output count rates scale with matrix size in boson sampling, including the effects of losses.

Findings

Output count rates scale predictably with matrix size.

Verification of nonclassical behavior remains feasible at large n.

Losses do not prevent the scaling laws from applying.

Abstract

Boson sampling is the problem of generating a quantum bit stream whose average is the permanent of a $n\times n$ matrix. The bitstream is created as the output of a prototype quantum computing device with $n$ input photons. It is a fundamental challenge to verify boson sampling, and the question of how output count rates scale with matrix size $n$ is crucial. Here we apply results from random matrix theory to establish scaling laws for average count rates in boson sampling experiments with arbitrary inputs and losses. The results show that, even with losses included, verification of nonclassical behaviour at large $n$ values is indeed possible.