# Classical Modeling of a Lossy Gaussian Bosonic Sampler

## TL;DR

This paper presents a classical algorithm to simulate a type of quantum computing experiment called Gaussian boson sampling, showing it can be efficiently simulated under certain conditions.

## Contribution

The novel contribution is a polynomial-time classical algorithm for lossy Gaussian boson sampling using Taylor series expansion.

## Key findings

- The algorithm's accuracy improves with more terms in the Taylor series expansion.
- The algorithm is efficient when the input state squeezing and loss level meet specific conditions.
- Recent quantum advantage experiments can be classically simulated using this method.

## Abstract

Gaussian boson sampling (GBS) is considered a candidate problem for demonstrating quantum advantage. We propose an algorithm for the approximate classical simulation of a lossy GBS instance. The algorithm relies on the Taylor series expansion, and increasing the number of terms of the expansion that are used in the calculation yields greater accuracy. The complexity of the algorithm is polynomial in the number of modes given the number of terms is fixed. We describe conditions for the input state squeezing parameter and loss level that provide the best efficiency for this algorithm (by efficient, we mean that the Taylor series converges quickly). In recent experiments that claim to have demonstrated quantum advantage, these conditions are satisfied; thus, this algorithm can be used to classically simulate these experiments.