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The optimization of circuit parameters of variational quantum algorithms suchas the variational quantum eigensolver (VQE) or the quantum approximateoptimization algorithm (QAOA) is a key challenge for the practical deploymentof near-term quantum computing algorithms. Here, we develop a hybridquantum/classical optimization procedure inspired by the Jacobi diagonalizationalgorithm for classical eigendecomposition, and combined with Andersonacceleration. In the first stage, analytical tomography fittings are performedfor a local cluster of circuit parameters via sampling of the observableobjective function at quadrature points in the circuit angles. Classicaloptimization is used to determine the optimal circuit parameters within thecluster, with the other circuit parameters frozen. Different clusters ofcircuit parameters are then optimized in "sweeps,'' leading to amonotonically-convergent fixed-point procedure. In the second stage, theiterative history of the fixed-point Jacobi procedure is used to accelerate theconvergence by applying Anderson acceleration/Pulay's direct inversion of theiterative subspace (DIIS). This Jacobi+Anderson method is numerically testedusing a quantum circuit simulator (without noise) for a representative testcase from the multistate, contracted variant of the variational quantumeigensolver (MC-VQE), and is found to be competitive with and often faster thanPowell's method and L-BFGS.

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