# Classical simulation of boson sampling with sparse output

## TL;DR

This paper presents efficient classical methods for simulating sparse boson sampling outputs by leveraging known marginal distributions, enabling feasible recovery of joint distributions in certain cases.

## Contribution

It introduces classical algorithms for simulating sparse boson sampling outputs, exploiting sparsity and marginal distributions, with extensions involving quantum annealing.

## Key findings

- Efficient classical recovery of joint distributions from sparse boson sampling data.
- Sparsity enables classical simulation where direct computation is complex.
- Extensions include quantum annealing approaches.

## Abstract

Boson sampling can simulate physical problems for which classical simulations are inefficient. However, not all problems simulated by boson sampling are classically intractable. We consider a situation in which it is known that the outcome from boson sampling is sparse. It can be determined from a few marginal distributions which are classically calculable. Still, recovering of the joint distribution can be of high complexity. We show classically efficient methods of the recovery assuming high sparsity of the joint distribution. Various extensions are discussed including a version involving quantum annealing.