Performance of hybrid quantum/classical variational heuristics for combinatorial optimization

TL;DR

This paper evaluates the practical performance of hybrid quantum/classical variational algorithms for solving combinatorial optimization problems, highlighting challenges and insights from numerical simulations.

Contribution

It provides empirical analysis of how different classical optimization methods perform in hybrid quantum algorithms for combinatorial problems, with insights on entanglement and Hamiltonian complexity.

Findings

Global optimization methods outperform local ones.

Hamiltonians with many Pauli terms are harder to optimize.

Entanglement does not show clear advantages in the studied variational forms.

Abstract

The recent literature on near-term applications for quantum computers contains several examples of the applications of hybrid quantum/classical variational approaches. This methodology can be applied to a variety of optimization problems, but its practical performance is not well studied yet. This paper moves some steps in the direction of characterizing the practical performance of the methodology, in the context of finding solutions to classical combinatorial optimization problems. Our study is based on numerical results obtained applying several classical nonlinear optimization algorithms to Hamiltonians for six combinatorial optimization problems; the experiments are conducted via noise-free classical simulation of the quantum circuits implemented in Qiskit. We empirically verify that: (1) finding the ground state is harder for Hamiltonians with many Pauli terms; (2) classical global optimization methods are more successful than local methods due to their ability of avoiding the numerous local optima; (3) there does not seem to be a clear advantage in introducing entanglement in the variational form.