Distinguishing noisy boson sampling from classical simulations

Valery Shchesnovich

doi:10.22331/q-2021-03-29-423

Abstract

Giving a convincing experimental evidence of the quantum supremacy over classical simulations is a challenging goal. Noise is considered to be the main problem in such a demonstration, hence it is urgent to understand the effect of noise. Recently found classical algorithms can efficiently approximate, to any small error, the output of boson sampling with finite-amplitude noise. In this work it is shown analytically and confirmed by numerical simulations that one can efficiently distinguish the output distribution of such a noisy boson sampling from the approximations accounting for low-order quantum multiboson interferences, what includes the mentioned classical algorithms. The number of samples required to tell apart the quantum and classical output distributions is strongly affected by the previously unexplored parameter: density of bosons, i.e., the ratio of total number of interfering bosons to number of input ports of interferometer. Such critical dependence is strikingly reminiscent of the quantum-to-classical transition in systems of identical particles, which sets in when the system size scales up while density of particles vanishes.

Highlights

Quantum mechanics promises computational advantage over digital computers [1, 2]
Always present in an experimental setup, compromise the quantum supremacy by allowing for an efficient classical simulation [10]? In this work we consider how a noisy boson sampling system can be distinguished from efficient classical approximations
In the spirit of Ref. [1], we have asked if a quantum system realizing imperfect/noisy boson sampling [4] can be efficiently and faithfully simulated classically as the system size scales up

Summary

Introduction

Quantum mechanics promises computational advantage over digital computers [1, 2]. Current technology is on the brink of building quantum devices with the promised advantage in some specific computational tasks, called the quantum supremacy [3], for which goal several quantum systems are considered [4, 5, 6, 7, 8] and a dramatic breakthrough was recently reported. As a partial answer to the above problem, in the present work it is shown that one can efficiently distinguish the output distribution of noisy boson sampling from output distributions of a wide range of classical algorithms, such as simulation with classical particles and the recent algorithms of Refs. [54] by considering a wide class of possible classical approximations to a noisy realization of boson sampling with arbitrary scaling of the interferometer size in the total number of interfering bosons, beyond the no-collision regime. The derivations and mathematical details are relegated to Appendices A-F

Noisy boson sampling vs classical approximations

Discussion of the results

A Lower bound for uniformly lossy interferometer

D Estimating the probability P1

E Numerical simulations of the lower bound