Quantum Approximate Optimization: A Computational Intelligence Perspective

TL;DR

This paper introduces quantum approximate optimization algorithms (QAOA) to the computational intelligence community, explaining their relevance, construction, and potential for solving combinatorial problems on near-term quantum devices.

Contribution

It provides an accessible overview of QAOA, its connections to CI, and practical implementation examples for common optimization problems.

Findings

QAOA can be applied to maximum cut, maximum bisection, and traveling salesperson problems.

Hybrid quantum-classical techniques can enhance QAOA performance.

QAOA offers a promising approach for near-term quantum optimization on noisy devices.

Abstract

Quantum computing is an emerging field on the multidisciplinary interface between physics, engineering, and computer science with the potential to make a large impact on computational intelligence (CI). The aim of this paper is to introduce quantum approximate optimization methods to the CI community because of direct relevance to solving combinatorial problems. We introduce quantum computing and variational quantum algorithms (VQAs). VQAs are an effective method for the near-term implementation of quantum solutions on noisy intermediate-scale quantum (NISQ) devices with less reliable qubits and early-stage error correction. Then, we explain Farhi et al.'s quantum approximate optimization algorithm (Farhi's QAOA, to prevent confusion). This VQA is generalized by Hadfield et al. to the quantum alternating operator ansatz (QAOA), which is a nature-inspired (particularly, adiabatic) quantum metaheuristic for approximately solving combinatorial optimization problems on gate-based quantum computers. We discuss connections of QAOA to relevant domains, such as computational learning theory and genetic algorithms, discussing current techniques and known results regarding hybrid quantum-classical intelligence systems. We present a schematic of how QAOA is constructed, and also discuss how CI techniques can be used to improve QAOA. We conclude with QAOA implementations for the well-known maximum cut, maximum bisection, and traveling salesperson problems, which can serve as templates for CI practitioners interested in using QAOA.