# Classically simulating near-term partially-distinguishable and lossy boson sampling

## TL;DR

This paper presents a new classical simulation method for Boson Sampling with partial distinguishability and loss, achieving polynomial runtime improvements over existing approaches in realistic experimental scenarios.

## Contribution

The authors develop a classical simulation scheme for Boson Sampling with partial distinguishability and loss, offering significant runtime improvements in practical regimes.

## Key findings

- Polynomial runtime improvement over ideal Boson Sampling simulation.
- Enhanced efficiency in simulating realistic, lossy, and partially distinguishable Boson Sampling.
- Applicable to near-term quantum experiments, challenging claims of quantum supremacy.

## Abstract

Boson Sampling is the problem of sampling from the same distribution as indistinguishable single photons at the output of a linear optical interferometer. It is an example of a non-universal quantum computation which is believed to be feasible in the near term and cannot be simulated on a classical machine. Like all purported demonstrations of "quantum supremacy", this motivates optimizing classical simulation schemes for a realistic model of the problem, in this case Boson Sampling when the implementations experience lost or distinguishable photons. Although current simulation schemes for sufficiently imperfect boson sampling are classically efficient, in principle the polynomial runtime can be infeasibly large. In this work, we develop a scheme for classical simulation of Boson Sampling under uniform distinguishability and loss, based on the idea of sampling from distributions where at most k photons are indistinguishable. We show that asymptotically this scheme can provide a polynomial improvement in the runtime compared to classically simulating idealised Boson Sampling. More significantly, we show that in the regime considered experimentally relevant, our approach gives an substantial improvement in runtime over other classical simulation approaches.