A Complex-Valued Continuous-Variable Quantum Approximation Optimization Algorithm (CCV-QAOA)

TL;DR

The paper introduces CCV-QAOA, a variational quantum algorithm operating in the complex domain, capable of efficiently solving a wide range of real and complex optimization problems using continuous-variable quantum systems.

Contribution

It presents the first complex-valued CV-QAOA framework, demonstrating its versatility across diverse optimization tasks including convex, non-convex, and constrained problems.

Findings

Successfully applied CCV-QAOA to convex quadratic minimization.

Performed scaling studies with circuit depth and cutoff dimension.

Achieved solutions for complex non-convex benchmarks like Styblinski-Tang.

Abstract

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.