固定置信度的量子蒙特卡洛树搜索
Quantum Monte Carlo Tree Search with Fixed Confidence
- Fudan University（复旦大学）
- Georgia Institute of Technology（佐治亚理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出量子MCTS算法（QMCTS），结合阈值消除与量子蒙特卡洛估计，在固定置信度下高效识别近似最优动作，并给出查询复杂度上下界及实验验证。
AI中文摘要：
量子计算的最新进展为计算密集型决策问题带来了新的机遇。本文研究了在固定置信度设置下，量子计算如何改进蒙特卡洛树搜索（MCTS），其目标是在给定博弈树中以高概率识别近似最优动作，同时最小化查询复杂度。我们首先在量子预言机模型下形式化MCTS。然后，我们开发了一种量子MCTS算法（QMCTS），该算法将搜索树上的阈值消除与量子蒙特卡洛估计相结合，以降低评估随机叶节点值的成本。我们建立了查询复杂度的实例相关下界，并推导了QMCTS的相应上界。下界分析引入了一个新的量子相位测试结果，该结果可能对MCTS之外的问题也有用。我们通过模拟实验验证了理论结果，并进一步在真实量子硬件上证明了QMCTS的可行性。
英文摘要：
Recent advances in quantum computing are opening new opportunities for computationally intensive decision problems. This paper studies how quantum computing can improve Monte Carlo tree search (MCTS) in the fixed-confidence setting, where the goal is to identify a near-optimal move in a given game tree with high probability while minimizing query complexity. We first formulate MCTS under a quantum oracle model. We then develop a quantum MCTS algorithm (QMCTS) that combines threshold-based elimination on the search tree with quantum Monte Carlo estimation to reduce the cost of evaluating stochastic leaf values. We establish an instance-dependent lower bound on the query complexity and derive a corresponding upper bound for QMCTS. The lower-bound analysis introduces a new quantum phase-testing result that may also be useful beyond MCTS. We validate the theoretical results through simulation experiments and further demonstrate the feasibility of QMCTS on real quantum hardware.
