On the Impact of Coordinate Descent for Multi-Angle QAOA in the Independent Set Graph Problem

Abstract

Constrained combinatorial optimisation provides a mathematical framework for modelling a wide range of practical decision making problems, including energy network operation, financial portfolio optimisation, logistics, routing, and resource allocation. This paper studies parameter optimisation for the multi angle quantum approximate optimisation algorithm (maQAOA) applied to the maximum independent set problem, a canonical constrained graph based optimisation task. We propose a coordinate wise training framework for maQAOA that updates one variational parameter at a time by solving a sequence of one dimensional optimisation subproblems. For each selected coordinate, the method reconstructs the objective dependence on that parameter and moves directly to the parameter value that minimises the training objective, or equivalently maximises the corresponding expected solution quality. While demonstrated specifically on maQAOA, the underlying theoretical principle, that the expectation value with respect to a given parameter can be analytically expressed as a finite Fourier series, is broadly applicable to general tasks solved via parameterised quantum circuits. Empirical evaluations on connected ErdHos Renyi graph benchmarks demonstrate that this analytic approach significantly reduces the computational training cost required to reach target approximation ratios and yields superior convergence reliability compared to standard gradient based, stochastic, and derivative free baselines.