发表机构
School of Management, Fudan University（复旦大学管理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究固定预算下量子计算对离散仿真优化的加速，提出首个量子算法QUEST，结合量子蒙特卡洛与序贯消除，证明其达到速率最优（预算依赖二次改进），数值实验验证其优于经典算法。
AI 中文摘要
近年来，量子计算发展迅速，并在多个领域展现出相对于经典计算的潜在优势。本文研究在固定预算设定下，量子计算能否加速离散仿真优化的收敛速率。我们首先通过定义量子仿真预言机、算法性能度量以及相应的最优性保证，来形式化量子离散仿真优化问题。基于这一形式化，我们为任何量子算法建立了期望最优性差距的极小极大下界。该下界分析将离散仿真优化问题简化为一个序贯量子相位测试问题，所得的下界论证可能具有独立的研究价值。通过将量子下界与其经典对应物进行比较，我们表明量子设定下的最优收敛速率在其对仿真预算的依赖上呈现出二次改进，但代价是对决策数量的依赖变差。随后，我们提出了首个固定预算量子算法，名为QUEST，用于离散仿真优化。该算法将量子蒙特卡洛子程序与序贯消除框架相结合，并采用慢测量机制以在优化过程中帮助保持量子叠加态。我们证明QUEST在达到对数因子范围内实现了最优收敛速率。数值实验进一步表明，QUEST优于其经典对应算法，这为量子在提升离散仿真优化算法收敛速率方面的优势提供了经验证据。
英文摘要
Quantum computing has developed rapidly in recent years and has shown potential advantages over classical computing in various domains. In this paper, we study whether quantum computing can accelerate the convergence rate of discrete simulation optimization in the fixed-budget setting. We first formulate the quantum discrete simulation optimization problem by defining the quantum simulation oracle, the algorithmic performance measure, and the corresponding optimality guarantee. Based on this formulation, we establish a minimax lower bound on the expected optimality gap for any quantum algorithm. The lower bound analysis reduces the discrete simulation optimization problem to a sequential quantum phase-testing problem, and the resulting lower-bound argument may be of independent interest. By comparing the quantum lower bound with its classical counterpart, we show that the optimal convergence rate in the quantum setting exhibits a quadratic improvement in its dependence on the simulation budget, at the cost of a worse dependence on the number of decisions. We then propose the first fixed-budget quantum algorithm, called \textsc{QUEST}, for discrete simulation optimization. The algorithm combines a quantum Monte Carlo subroutine with a sequential elimination framework and uses a slow-measurement mechanism to help preserve quantum superposition during the optimization process. We prove that \textsc{QUEST} achieves the optimal convergence rate up to logarithmic factors. Numerical experiments further show that \textsc{QUEST} outperforms its classical counterpart, which provides empirical evidence for the quantum advantage in improving the convergence rate of discrete simulation optimization algorithms.
