Noise thresholds for classical simulability of non-linear Boson sampling

TL;DR

This paper investigates how adding non-linearities, specifically Kerr effects, to Boson sampling enhances its robustness against noise, potentially making classical simulation more difficult and aiding experimental demonstration of quantum advantage.

Contribution

It introduces a method to incorporate higher order non-linearities into Boson sampling, increasing noise thresholds for classical simulability and providing a non-classicality condition for quantum advantage.

Findings

Adding Kerr non-linearity improves noise robustness.

Higher non-linearities increase classical simulation thresholds.

A phase-space negativity criterion for non-classicality is established.

Abstract

Boson sampling, a computational problem conjectured to be hard to simulate on a classical machine, is a promising candidate for an experimental demonstration of quantum advantage using bosons. However, inevitable experimental noise and imperfections, such as loss in the interferometer and random counts at the detectors, could challenge the sampling task from entering the regime where quantum advantage is achievable. In this work we introduce higher order non-linearities as a mean to enhance the computational complexity of the problem and the protocol's robustness against noise, i.e. increase the noise threshold that allows to perform an efficient classical simulation of the problem. Using a phase-space method based on the negativity volume of the relevant quasi-probability distributions, we establish a necessary non-classicality condition that any experimental proof of quantum advantage must satisfy. Our results indicate that the addition of single-mode Kerr non-linearity at the input state preparation level, while retaining a linear-optical evolution, makes the Boson sampling protocol more robust against noise and consequently relaxes the constraints on noise parameters required to show quantum advantage.