发表机构
School of Aeronautics and Astronautics, Purdue University（普渡大学航空航天学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究将模型预测路径积分控制（MPPI）的更新转化为量子查询问题，通过量子振幅估计实现了较经典蒙特卡洛采样的二次查询效率提升，相关示例验证了其估计器缩放特性。
AI 中文摘要
模型预测路径积分控制（MPPI）通过代价加权的轨迹样本计算更新，在稀有事件或高精度场景中可能需要大量经典滚动。我们将有限集合MPPI更新的每个分量重新表述为有界路径期望的比率，构造可逆滚动预言机将其编码为成功概率，使更新可直接通过量子振幅估计进行估算。这相较于经典蒙特卡洛采样，在精度和稀有事件需求的查询依赖上实现了二次提升，匹配了穷举评估阈值以下基础标量问题的已知下界，而我们的逐坐标构造会产生与控制输入数量成线性的依赖。对于固定集合，低温权重集中在最低代价轨迹上，当最小值唯一时，将极限控制与量子最小查找关联起来。一个完全可枚举的制导示例验证了预测的估计器缩放关系，且带有交叉条件的说明性操作计数模型将查询优势与建模实现优势区分开。
英文摘要
Model predictive path integral (MPPI) control computes its inputs as cost-weighted averages over simulated trajectories. However, it typically requires many simulations, especially when low-cost trajectories are rare. We therefore formulate this computation as a quantum query problem. By replacing Gaussian input perturbations with random signs, we express the MPPI update as a ratio of averages over a finite set of perturbation sequences. We then construct quantum circuits that encode these averages as measurement probabilities, which allows quantum amplitude estimation to compute the update with fewer queries than classical sampling. Numerical examples confirm the predicted query scalings and show that a quantum advantage requires many perturbation sequences.
Comments6 pages, submitted to LCSS+ACC_2027
