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

@misc{ruiz2026binary,
  title = {{Binary Optimization with Complex Constraints via Quantum Approximate Multi-Objective Optimization}},
  author = {Andres Ruiz and Soumyadip Ghosh and Stefan Woerner},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.13790},
  eprint = {2609.13790},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13790},
  note = {CC BY-NC-ND 4.0},
}

TY  - UNPB
TI  - Binary Optimization with Complex Constraints via Quantum Approximate Multi-Objective Optimization
AU  - Andres Ruiz
AU  - Soumyadip Ghosh
AU  - Stefan Woerner
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2609.13790
UR  - https://arxiv.org/abs/2609.13790
AB  - 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.
ER  -