Classical simulability of constant-depth linear-optical circuits with noise

TL;DR

This paper demonstrates that noise in shallow-depth linear-optical circuits, such as photon loss and partial distinguishability, can make these systems efficiently simulable classically by analyzing their graph structure and percolation thresholds.

Contribution

The work establishes a novel correspondence between linear-optical circuits and bipartite graphs, showing how noise thresholds lead to efficient classical simulation of shallow-depth quantum optical systems.

Findings

Photon loss and distinguishability effects are equivalent to vertex removal in the graph model.

Above a certain noise threshold, circuits can be decomposed into smaller, classically simulable systems.

Shallow-depth circuits with noise can be efficiently simulated classically due to their entanglement structure.

Abstract

Noise is one of the main obstacles to realizing quantum devices that achieve a quantum computational advantage. A possible approach to minimize the noise effect is to employ shallow-depth quantum circuits since noise typically accumulates as circuit depth grows. In this work, we investigate the complexity of shallow-depth linear-optical circuits under the effects of photon loss and partial distinguishability. By establishing a correspondence between a linear-optical circuit and a bipartite graph, we show that the effects of photon loss and partial distinguishability are equivalent to removing the corresponding vertices. Using this correspondence and percolation theory, we prove that for constant-depth linear-optical circuits with single photons, there is a threshold of loss (noise) rate above which the linear-optical systems can be decomposed into smaller systems with high probability, which enables us to simulate the systems efficiently. Consequently, our result implies that even in shallow-depth circuits where noise is not accumulated enough, its effect may be sufficiently significant to make them efficiently simulable using classical algorithms due to its entanglement structure constituted by shallow-depth circuits.