Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information

TL;DR

This paper introduces a stochastic approximation method to efficiently estimate the Quantum Fisher Information matrix, reducing computational costs in high-dimensional quantum parameter spaces.

Contribution

It proposes a novel simultaneous perturbation stochastic approximation algorithm for QFIM estimation, enabling constant-cost computation in complex quantum models.

Findings

Efficient QFIM approximation with reduced computational complexity.

Successful application to Hamiltonian ground state preparation.

Effective training of Variational Quantum Boltzmann Machines.

Abstract

The Quantum Fisher Information matrix (QFIM) is a central metric in promising algorithms, such as Quantum Natural Gradient Descent and Variational Quantum Imaginary Time Evolution. Computing the full QFIM for a model with $d$ parameters, however, is computationally expensive and generally requires $\mathcal{O}(d^2)$ function evaluations. To remedy these increasing costs in high-dimensional parameter spaces, we propose using simultaneous perturbation stochastic approximation techniques to approximate the QFIM at a constant cost. We present the resulting algorithm and successfully apply it to prepare Hamiltonian ground states and train Variational Quantum Boltzmann Machines.