Treffer: The Impact of Optimization Approximation Algorithms on the Performance of BHT-QAOA

This article investigates the impact of five optimization approximation algorithms on our previously introduced Boolean-Hamiltonians Transform for Quantum Approximate Optimization Algorithm (BHT-QAOA) using two performance metrics. These algorithms are BFGS, L-BFGS-B, SLSQP, COBYLA, and COBYQA. The performance of such an impact is evaluated and compared using two metrics: the final number of function evaluations for an algorithm, and the final quality of qubits measurement for all best-approximated solutions for a problem. A set of arbitrary classical Boolean problems in various logical structures was examined and evaluated using BHT-QAOA, five approximation algorithms, and an IBM quantum computer. Broadly, the BHT-QAOA with these five classical approximation algorithms successfully finds all optimized approximated solutions for these problems. Specifically, both BFGS and SLSQP approximation algorithms successfully search for all best-approximated solutions for these problems, in the context of fewer number of function evaluations and higher quality of qubits measurement, in the hybrid classical-quantum domain.