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

• URL: http://arxiv.org/abs/2609.13790v1
• Date: Sat, 12 Sep 2026 08:07:15 GMT
• Title: Binary Optimization with Complex Constraints via Quantum Approximate Multi-Objective Optimization
• Abstract summary: 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.<n>We demonstrate the approach for binary portfolio optimization under a Conditional Value-at-Risk constraint.
• Score: 1.3827807729367585
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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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