Classical simulation of Gaussian quantum circuits with non-Gaussian input states

TL;DR

This paper establishes conditions under which Gaussian quantum circuits with non-Gaussian inputs can be efficiently simulated classically, by extending the stellar representation and linking non-Gaussianity to simulation complexity.

Contribution

It generalizes the stellar representation to multimode states and connects stellar rank to classical simulation cost for non-Gaussian input states.

Findings

Efficient classical simulation is possible under certain conditions.

Stellar rank quantifies non-Gaussianity and influences simulation complexity.

Results impact the understanding of near-term continuous-variable quantum circuits.

Abstract

We consider Gaussian quantum circuits supplemented with non-Gaussian input states and derive sufficient conditions for efficient classical strong simulation of these circuits. In particular, we generalise the stellar representation of continuous-variable quantum states to the multimode setting and relate the stellar rank of the input non-Gaussian states, a recently introduced measure of non-Gaussianity, to the cost of evaluating classically the output probability densities of these circuits. Our results have consequences for the strong simulability of a large class of near-term continuous-variable quantum circuits.