变分量子本征求解器中序列最小优化的先验信息自适应偏移
Prior-Informed Adaptive Shifts for Sequential Minimal Optimization in Variational Quantum Eigensolvers
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中文总结 AI 辅助
该研究针对变分量子本征求解器序列最小优化的测量位置问题，提出先验信息自适应偏移方法，通过结合极小值点先验信息优化测量位置，经数值实验验证其有效性。
中文摘要 AI 辅助
序列最小优化方法，如Rotosolve算法和Nakanishi-Fujii-Todo算法（NFT），被广泛应用于变分量子本征求解器（VQE）。这些方法每次优化一个参数方向，仅需在该方向上的少数位置进行测量。然而，在存在测量散粒噪声的情况下，它们的性能关键取决于测量位置的选择，近期研究表明等距测量是最优的。但我们常观察到，实际中等距测量并不总是最优的。我们认为，理论与实践之间的这种差异源于先前分析的两个假设通常不成立：（1）缺乏关于能量极小值点的先验知识；（2）使用估计能量的不确定性作为优化性能的替代指标。本文中，我们开发了一种确定最优测量位置的新理论。首先，我们证明结合关于极小值点的先验信息是有益的：在优化初期，当对当前极小值点（即枢轴）知之甚少时，等距测量确实接近最优；但随着先验信念变得明确，最优位置会偏离等距。其次，我们不再分析估计最小能量的不确定性，而是研究极小值点估计量本身的不确定性，这会导致显著不同的策略。基于此分析，我们提出了先验信息自适应偏移（PAS）方法，该方法在优化过程中自动调整测量位置。针对不同散粒数和问题的数值实验验证了我们的理论发现，并证明PAS能在每种机制中自适应恢复最优的固定偏移，无需预先指定。
英文摘要
Sequential minimal optimization methods, such as the Rotosolve and the Nakanishi-Fujii-Todo algorithm (NFT), are widely used for Variational Quantum Eigensolvers (VQEs). These methods optimize one parameter direction at a time, requiring measurements at only a few locations along that direction. In the presence of measurement shot noise, however, their performance depends critically on the choice of measurement locations, and recent studies suggest that equidistant measurements are optimal. However, we often observe that equidistant measurements are not always optimal in practice. We argue that this discrepancy between theory and practice arises from the fact that two assumptions underlying previous analyses do not generally hold: (1) the absence of prior knowledge about the energy minimizer, and (2) the use of the uncertainty of the estimated energy as a proxy for optimization performance. In this paper, we develop a new theory for determining optimal measurement locations. First, we show that incorporating prior information about the minimizer is beneficial. Early in optimization, when little is known about the pivot, i.e., the current minimizer, equidistant measurements are indeed near-optimal, but as the prior belief sharpens the optimal locations move away from equidistant. Second, rather than analyzing the uncertainty of the estimated minimum energy, we study the uncertainty of the estimator of the minimizer itself, which leads to substantially different strategies. Based on this analysis, we propose Prior-informed Adaptive Shifts (PAS), a method that automatically adjusts measurement locations during optimization. Numerical experiments across different shot counts and problems validate our theoretical findings and demonstrate that PAS adaptively recovers whichever fixed shift is best in each regime without it being specified in advance.
