# Regimes of classical simulability for noisy Gaussian boson sampling

## TL;DR

This paper establishes a classical simulation threshold for noisy Gaussian Boson Sampling, showing how noise and loss affect quantum advantage and proposing input squeezing as a mitigation strategy.

## Contribution

It formalizes a sufficient condition for classical simulability of noisy GBS and analyzes how noise impacts quantum advantage in linear-optical architectures.

## Key findings

- Noisy GBS becomes classically simulable under certain noise conditions.
- Quantum advantage diminishes with exponential photon loss in deep circuits.
- Increasing input squeezing can help GBS evade classical simulation.

## Abstract

As a promising candidate for exhibiting quantum computational supremacy, Gaussian Boson Sampling (GBS) is designed to exploit the ease of experimental preparation of Gaussian states. However, sufficiently large and inevitable experimental noise might render GBS classically simulable. In this work, we formalize this intuition by establishing a sufficient condition for approximate polynomial-time classical simulation of noisy GBS --- in the form of an inequality between the input squeezing parameter, the overall transmission rate and the quality of photon detectors. Our result serves as a non-classicality test that must be passed by any quantum computationalsupremacy demonstration based on GBS. We show that, for most linear-optical architectures, where photon loss increases exponentially with the circuit depth, noisy GBS loses its quantum advantage in the asymptotic limit. Our results thus delineate intermediate-sized regimes where GBS devices might considerably outperform classical computers for modest noise levels. Finally, we find that increasing the amount of input squeezing is helpful to evade our classical simulation algorithm, which suggests a potential route to mitigate photon loss.