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

Abstract

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