发表机构
IBM Research（IBM研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出将复杂约束的二元优化转化为多目标QUBO，利用量子近似多目标优化在100资产组合上逼近帕累托前沿，并通过经典后处理获得可行解。
AI 中文摘要
我们证明，一类具有复杂非二次目标或约束的二元优化问题可以重新表述为多目标二次无约束二元优化问题。当目标和约束依赖于少量二次特征，并相对于其偏好方向单调时，至少有一个全局最优解位于相关MO-QUBO的帕累托集中。这使得约束可以在帕累托最优候选上经典地评估，而非编码为惩罚项。我们针对带有条件风险价值约束的二元投资组合优化展示了该方法。使用量子近似多目标优化，在一个示例性的100资产实例上，我们利用IBM量子计算机近似均值-方差帕累托前沿，并通过经典后处理推导出均值-CVaR前沿。硬件结果恢复了经典前沿的整体结构，并为不同的风险界限生成了接近最优的可行投资组合。
英文摘要
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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