Quantum circuit evolutionary framework applied on set partitioning problem

TL;DR

This paper introduces a quantum circuit evolutionary framework with variable topology, demonstrating promising results in solving set partitioning problems and avoiding convergence issues common in variational algorithms.

Contribution

It proposes a novel framework combining ansatz-free and physics-inspired circuit structures to enhance quantum optimization without classical optimizers.

Findings

Pseudo-counterdiabatic approach avoids convergence stagnation

Variable topology circuits outperform traditional methods in noisy scenarios

Framework shows potential for large-scale integer optimization

Abstract

Quantum algorithms are of great interest for their possible use in optimization problems. In particular, variational algorithms that use classical counterparts to optimize parameters hold promise for use in currently existing devices. However, convergence stagnation phenomena pose a challenge for such algorithms. Seeking to avoid such difficulties, we present a framework based on circuits with variable topology with two approaches, one based on ansatz-free evolutionary method known from literature and the other using an introduction of an ansatz with circuital structure inspired by the physics of the Hamiltonian related to the problem, considering a, named here, pseudo-counterdiabatic evolutionary term. The efficiency of the proposed framework was tested on several instances of the set partitioning problem. The two approaches were compared with the Variational Quantum Eigensolver in noisy and non-noisy scenarios. The results demonstrated that optimization using circuits with variable topology presented very encouraging results. Notably, the strategy employing a pseudo-counterdiabatic evolutionary term exhibited remarkable performance, avoiding convergence stagnation in most instances considered. This framework circumvents the need for classical optimizers, and, as a consequence, this procedure based on circuits with variable topology indicates an interesting path in the search for algorithms to solve integer optimization problems targeting efficient applications in larger-scale scenarios.