通过自适应控制测量次数，提升量子变分算法的优化效率
Adaptive Observation Cost Control for Variational Quantum Eigensolvers
- 用高斯过程预测优化区域，动态调整每轮测量次数
- 在保证精度前提下，单次迭代测量次数减少至数百次以内
- 适合需要高效运行量子算法的研究者和开发者
变分量子本征求解器（VQE）的目标函数具有特定形式，可采用仅需少量观测的序列最小优化（SMO）方法。然而，由于测量噪声影响，每次观测通常需平均数百至数千次量子测量才能达到合理信噪比，导致计算成本高昂。本文提出一种自适应成本控制方法——子空间置信区域（SubsCoRe），基于高斯过程代理模型，确保更新子空间内不确定性低，从而保障每轮优化精度。该方法根据优化进展设定所需精度，并选择满足精度要求的最少测量次数及分布。实验表明，SubsCoRe 显著提升 SMO 效率，优于当前最优方法。
原文摘要 · Abstract (English)
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.
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