From Theory to Practice: Analyzing Variational Quantum Power Method for Quantum Optimization of QUBO Problems

TL;DR

This paper provides a comprehensive analysis of the variational quantum power method (VQPM) for quantum optimization of QUBO problems, including convergence, robustness, and practical application strategies, supported by numerical simulations and comparisons with QAOA.

Contribution

It offers a detailed theoretical and numerical evaluation of VQPM, introduces practical strategies for applying it to QUBO problems, and compares its performance with QAOA in noisy environments.

Findings

VQPM is effective for quantum optimization of QUBO problems.

Strategies leveraging qubit locking improve VQPM performance.

VQPM shows competitive results compared to QAOA in noisy simulations.

Abstract

The variational quantum power method (VQPM), which adapts the classical power iteration algorithm for quantum settings, has shown promise for eigenvector estimation and optimization on quantum hardware. In this work, we provide a comprehensive theoretical and numerical analysis of VQPM by investigating its convergence, robustness, and qubit locking mechanisms. We present detailed strategies for applying VQPM to QUBO problems by leveraging these locking mechanisms. Based on the simulations for each strategy we have carried out, we give systematic guidelines for their practical applications. We also offer a numerical comparison with the quantum approximate optimization algorithm (QAOA) by running both algorithms on a set of trial problems and a simulation on noisy environments by using IBM Qiskit Aer simulation framework. Our results indicate that VQPM can be employed as an effective quantum optimization algorithm on quantum computers for QUBO problems, and this work can serve as an initial guideline for such applications.