Quantifying fermionic nonlinearity of quantum circuits

TL;DR

This paper introduces a measure called fermionic nonlinearity to evaluate how noise affects the classical simulability of quantum circuits simulating fermionic systems, aiding in the design of quantum algorithms with potential advantages.

Contribution

It proposes a new quantifier for fermionic circuit nonlinearity and demonstrates its application in assessing classical simulatability under noise conditions.

Findings

Fermionic nonlinearity varies with noise and system parameters.

Certain quantum circuits become classically simulatable under specific noise levels.

The method helps identify regimes where quantum advantage may be lost.

Abstract

Variational quantum algorithms (VQAs) have been proposed as one of the most promising approaches to demonstrate quantum advantage on noisy intermediate-scale quantum (NISQ) devices. However, it has been unclear whether VQAs can maintain quantum advantage under the intrinsic noise of the NISQ devices, which deteriorates the quantumness. Here we propose a measure, called fermionic nonlinearity, to quantify the classical simulatability of quantum circuits designed for simulating fermionic Hamiltonians. Specifically, we construct a Monte Carlo type classical algorithm based on the classical simulatability of fermionic linear optics, whose sampling overhead is characterized by the fermionic nonlinearity. As a demonstration of these techniques, we calculate the upper bound of the fermionic nonlinearity of a rotation gate generated by four fermionic modes under the dephasing noise. Moreover, we estimate the sampling costs of the unitary coupled cluster singles and doubles quantum circuits for hydrogen chains subject to the dephasing noise. We find that, depending on the error probability and atomic spacing, there are regions where the fermionic nonlinearity becomes very small or unity, and hence the circuits are classically simulatable. We believe that our method and results help to design quantum circuits for fermionic systems with potential quantum advantages.