Quantum computing fidelity susceptibility using automatic differentiation

TL;DR

This paper demonstrates how quantum automatic differentiation can be employed to compute fidelity susceptibility in quantum systems, incorporating error mitigation techniques and analyzing their impact on accuracy.

Contribution

It introduces a method combining quantum automatic differentiation with error mitigation to compute fidelity susceptibility, highlighting optimizations and noise effects in quantum simulations.

Findings

Successful simulation of fidelity susceptibility in the transverse-field Ising model

Error mitigation impacts the statistical noise in derivative computations

Optimizations improve the efficiency of quantum automatic differentiation

Abstract

Automatic differentiation is an invaluable feature of machine learning and quantum machine learning software libraries. In this work it is shown how quantum automatic differentiation can be used to solve the condensed-matter problem of computing fidelity susceptibility, a quantity whose value may be indicative of a phase transition in a system. Results are presented using simulations including hardware noise for small instances of the transverse-field Ising model, and a number of optimizations that can be applied are highlighted. Error mitigation (zero-noise extrapolation) is applied within the autodifferentiation framework to a number of gradient values required for computation of fidelity susceptibility and a related quantity, the second derivative of the energy. Such computations are found to be highly sensitive to the additional statistical noise incurred by the error mitigation method