A Jacobi Diagonalization and Anderson Acceleration Algorithm For Variational Quantum Algorithm Parameter Optimization

TL;DR

This paper introduces a hybrid quantum/classical optimization algorithm combining Jacobi diagonalization and Anderson acceleration to efficiently optimize variational quantum algorithms, demonstrating improved convergence speed over traditional methods.

Contribution

The paper presents a novel hybrid optimization method for variational quantum algorithms that integrates Jacobi diagonalization with Anderson acceleration, enhancing convergence efficiency.

Findings

The method is competitive with Powell's and L-BFGS algorithms.

It demonstrates faster convergence in numerical tests.

Applicable to variational quantum eigensolver variants.

Abstract

The optimization of circuit parameters of variational quantum algorithms such as the variational quantum eigensolver (VQE) or the quantum approximate optimization algorithm (QAOA) is a key challenge for the practical deployment of near-term quantum computing algorithms. Here, we develop a hybrid quantum/classical optimization procedure inspired by the Jacobi diagonalization algorithm for classical eigendecomposition, and combined with Anderson acceleration. In the first stage, analytical tomography fittings are performed for a local cluster of circuit parameters via sampling of the observable objective function at quadrature points in the circuit angles. Classical optimization is used to determine the optimal circuit parameters within the cluster, with the other circuit parameters frozen. Different clusters of circuit parameters are then optimized in "sweeps,'' leading to a monotonically-convergent fixed-point procedure. In the second stage, the iterative history of the fixed-point Jacobi procedure is used to accelerate the convergence by applying Anderson acceleration/Pulay's direct inversion of the iterative subspace (DIIS). This Jacobi+Anderson method is numerically tested using a quantum circuit simulator (without noise) for a representative test case from the multistate, contracted variant of the variational quantum eigensolver (MC-VQE), and is found to be competitive with and often faster than Powell's method and L-BFGS.