Optimal parameter range for QCGD searches

Determine the optimal parameter range for the QCGD step-size and conjugate-coefficient search for each system size of the Heisenberg model, so that the parameter grid captures the relevant energy minima and avoids restricting the algorithm’s performance.

Background

QCGD selects both the step size mu_k and conjugate coefficient gamma_k through a finite two-dimensional grid search. In the reported experiments, the restricted domain mu_k,gamma_k in[0,0.5] sometimes placed the selected minimum at the boundary, while extending the domain to [0,1.5] produced a substantially different optimum in at least one iteration.

Because the appropriate search domain may depend on the system size and optimization landscape, the paper does not establish a generally suitable parameter range. The authors explicitly identify determining that range as requiring future work.