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arXiv · 2609.13790

Binary Optimization with Complex Constraints via Quantum Approximate Multi-Objective Optimization

Andres Ruiz·Soumyadip Ghosh·Stefan Woerner
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Abstract

We show that a class of binary optimization problems with complex non-quadratic objectives or constraints can be reformulated as multi-objective quadratic unconstrained binary optimization problems. When the objective and constraints depend on a small number of quadratic features and are monotone with respect to their preferred directions, at least one globally optimal solution lies in the Pareto set of the associated MO-QUBO. This enables the constraints to be evaluated classically on Pareto-optimal candidates rather than encoded as penalties. We demonstrate the approach for binary portfolio optimization under a Conditional Value-at-Risk constraint. Using Quantum Approximate Multi-Objective Optimization on an illustrative 100-asset instance, we approximate the mean-variance Pareto front using an IBM Quantum computer and derive mean-CVaR fronts through classical post-processing. The hardware results recover the overall structure of the classical front and yield near-optimal feasible portfolios for different risk bounds.

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Andres Ruiz, Soumyadip Ghosh, Stefan Woerner. 2026-09-12. Binary Optimization with Complex Constraints via Quantum Approximate Multi-Objective Optimization. https://arxiv.org/abs/2609.13790

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