We develop a global variable substitution method that reduces n-variable monomials in combinatorial optimization problems to equivalent instances with monomials in fewer variables. We apply this technique to 3-SAT and analyze the optimal quantum circuit depth needed to solve the reduced problem using the quantum approximate optimization algorithm. For benchmark 3-SAT problems, we find that the upper bound of the circuit depth is smaller when the problem is formulated as a product and uses the substitution method to decompose gates than when the problem is written in the linear formulation, which requires no decomposition.
@article{arxiv.2108.03281,
title = {Globally optimizing QAOA circuit depth for constrained optimization problems},
author = {Rebekah Herrman and Lorna Treffert and James Ostrowski and Phillip C. Lotshaw and Travis S. Humble and George Siopsis},
journal= {arXiv preprint arXiv:2108.03281},
year = {2021}
}