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Theoretical Computer Science

Penalty-enhanced quantum approximate optimization algorithm framework for maximization and minimization problems

Hao Zhong, Qi Zhang

Published Nov 22, 2025• 0 citations
Publisher
DOI
10.1016/j.tcs.2025.115649

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Continuous-variable (CV) quantum systems offer a natural framework for continuous optimization through their infinite-dimensional Hilbert spaces. In this paper, we propose the Complex Continuous-Variable Quantum Approximate Optimization Algorithm (CCV-QAOA), a variational framework operating in the complex domain that optimizes over complex decision variables. The method efficiently solves real and complex multivariate optimization problems. To demonstrate its versatility, we apply CCV-QAOA across a broad suite of optimization use cases, including convex quadratic minimization, scaling studies with circuit depth and cutoff dimension, constrained quadratic programs using penalty constructions, and non-convex benchmarks such as the Styblinski-Tang function and complex quartic landscapes.
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