Gaussian boson sampling with partial distinguishability

TL;DR

This paper develops a model for Gaussian boson sampling with partial photon distinguishability, introducing an efficient classical simulation method that extends the boundary of quantum supremacy under realistic experimental conditions.

Contribution

It presents a novel framework and simulation algorithm for partially distinguishable GBS, enhancing understanding of realistic quantum advantage scenarios.

Findings

The model accurately describes partially distinguishable and lossy GBS.

The simulation algorithm reduces complexity exponentially with indistinguishability.

Partial distinguishability can extend the classical simulability boundary of GBS.

Abstract

Gaussian boson sampling (GBS) allows for a way to demonstrate quantum supremacy with the relatively modest experimental resources of squeezed light sources, linear optics, and photon detection. In a realistic experimental setting, numerous effects can modify the complexity of the sampling, in particular loss, partial distinguishability of the photons, and the use of threshold detectors rather than photon counting detectors. In this paper, we investigate GBS with partial distinguishability using an approach based on virtual modes and indistinguishability efficiency. We develop a model using these concepts and derive the probabilities of measuring a specific output pattern from partially distinguishable and lossy GBS for both types of detectors. In the case of threshold detectors, the probability as calculated by the Torontonian is a special case under our framework. By analyzing the expressions of these probabilities we propose an efficient auxiliary classical simulation algorithm which can be used to calculate the probabilities. Our model and the auxiliary algorithm provide foundations for an approximation method for the probability calculation and simulation algorithms not only compatible with existing state-of-the-art simulation algorithms for ideal GBS but also reduce their complexities exponentially depending on the indistinguishability. Using the approximation method and the simulation algorithms we show how the boundary of quantum supremacy in GBS can be pushed further by partial distinguishability.