标题： 变分量子本征求解器的自适应观测成本控制 显示英文标题

标题： Adaptive Observation Cost Control for Variational Quantum Eigensolvers

摘要： 变分量子本征求解器（VQE）中要最小化的目标具有受限形式，这允许一种专门的序列最小优化（SMO），每次迭代只需少量观测。 然而，由于观测噪声的存在，SMO迭代仍然成本高昂——在一点进行一次观测通常需要对数百到数千次重复的量子测量结果进行平均，以达到合理的噪声水平。 在本文中，我们提出了一种自适应成本控制方法，称为置信区域子空间（SubsCoRe），用于SMO。 SubsCoRe使用高斯过程（GP）代理模型，并要求其在被更新的子空间上具有低不确定性，从而确保每次迭代的优化具有保证的准确性。 自适应成本控制首先根据优化的进展设置所需精度，然后选择最少的测量次数及其分布，以满足所需的精度。 我们证明，SubsCoRe显著提高了SMO的效率，并优于最先进的方法。 显示英文摘要

摘要： The objective to be minimized in the variational quantum eigensolver (VQE) has a restricted form, which allows a specialized sequential minimal optimization (SMO) that requires only a few observations in each iteration. However, the SMO iteration is still costly due to the observation noise -- one observation at a point typically requires averaging over hundreds to thousands of repeated quantum measurement shots for achieving a reasonable noise level. In this paper, we propose an adaptive cost control method, named subspace in confident region (SubsCoRe), for SMO. SubsCoRe uses the Gaussian process (GP) surrogate, and requires it to have low uncertainty over the subspace being updated, so that optimization in each iteration is performed with guaranteed accuracy. The adaptive cost control is performed by first setting the required accuracy according to the progress of the optimization, and then choosing the minimum number of measurement shots and their distribution such that the required accuracy is satisfied. We demonstrate that SubsCoRe significantly improves the efficiency of SMO, and outperforms the state-of-the-art methods.