Classical simulations of noisy variational quantum circuits

TL;DR

This paper introduces LOWESA, a classical simulation algorithm for noisy variational quantum circuits, demonstrating its efficiency under certain conditions and analyzing its limitations and scalability.

Contribution

The paper presents LOWESA, a novel polynomial-time classical simulation method for noisy variational quantum circuits, combining spectral analysis, Pauli back-propagation, and recent noisy circuit simulation techniques.

Findings

LOWESA efficiently estimates expectation values with exponentially vanishing error in noise rate.

The algorithm is polynomial in qubits and depth under certain conditions.

Practical limitations arise for circuits with correlated parameters and low error rates.

Abstract

Noise detrimentally affects quantum computations so that they not only become less accurate but also easier to simulate classically as systems scale up. We construct a classical simulation algorithm, LOWESA (low weight efficient simulation algorithm), for estimating expectation values of noisy parameterised quantum circuits. It combines previous results on spectral analysis of parameterised circuits with Pauli back-propagation and recent ideas for simulations of noisy random circuits. We show, under some conditions on the circuits and mild assumptions on the noise, that LOWESA gives an efficient, polynomial algorithm in the number of qubits (and depth), with approximation error that vanishes exponentially in the physical error rate and a controllable cut-off parameter. We also discuss the practical limitations of the method for circuit classes with correlated parameters and its scaling with decreasing error rates.