# No imminent quantum supremacy by boson sampling

## TL;DR

This paper argues that achieving quantum supremacy through boson sampling is unlikely in the near term, as classical algorithms can simulate larger photon systems than current experiments, and technological improvements are needed.

## Contribution

The paper introduces advanced classical algorithms for boson sampling and provides analyses showing the difficulty of demonstrating quantum supremacy with current and near-term technology.

## Key findings

- Classical algorithms can simulate up to 30 photons in boson sampling.
- Current experiments with 5 photons are far from demonstrating supremacy.
- Photon losses significantly hinder the realization of quantum supremacy.

## Abstract

It is predicted that quantum computers will dramatically outperform their conventional counterparts. However, large-scale universal quantum computers are yet to be built. Boson sampling is a rudimentary quantum algorithm tailored to the platform of photons in linear optics, which has sparked interest as a rapid way to demonstrate this quantum supremacy. Photon statistics are governed by intractable matrix functions known as permanents, which suggests that sampling from the distribution obtained by injecting photons into a linear-optical network could be solved more quickly by a photonic experiment than by a classical computer. The contrast between the apparently awesome challenge faced by any classical sampling algorithm and the apparently near-term experimental resources required for a large boson sampling experiment has raised expectations that quantum supremacy by boson sampling is on the horizon. Here we present classical boson sampling algorithms and theoretical analyses of prospects for scaling boson sampling experiments, showing that near-term quantum supremacy via boson sampling is unlikely. While the largest boson sampling experiments reported so far are with 5 photons, our classical algorithm, based on Metropolised independence sampling (MIS), allowed the boson sampling problem to be solved for 30 photons with standard computing hardware. We argue that the impact of experimental photon losses means that demonstrating quantum supremacy by boson sampling would require a step change in technology.