用贝叶斯方法改进量子变分算法的梯度估计，提升优化速度。
Bayesian Parameter Shift Rule in Variational Quantum Eigensolvers
- 引入高斯过程建模梯度，支持任意位置观测并给出不确定性
- 在随机梯度下降中复用历史数据，加速收敛过程
- 结合置信区域机制，降低每步采样成本，适合资源受限场景
参数移位规则（PSR）是变分量子本征求解器（VQE）中高效梯度估计的关键技术。本文提出其贝叶斯变体：利用带有合适核函数的高斯过程来估计VQE目标函数的梯度。该贝叶斯PSR可从任意位置的观测中灵活推断梯度，并提供不确定性信息，在特定情况下退化为广义PSR。在随机梯度下降（SGD）中，贝叶斯PSR允许复用前步观测，加速优化进程。此外，通过获取后验不确定性，并结合提出的梯度置信区域（GradCoRe）概念，可最小化每步的观测开销。数值实验表明，采用贝叶斯PSR与GradCoRe的VQE优化显著加速了SGD，优于当前最先进的方法，包括序列最小优化（SMO）。
原文摘要 · Abstract (English)
Parameter shift rules (PSRs) are key techniques for efficient gradient estimation in variational quantum eigensolvers (VQEs). In this paper, we propose its Bayesian variant, where Gaussian processes with appropriate kernels are used to estimate the gradient of the VQE objective. Our Bayesian PSR offers flexible gradient estimation from observations at arbitrary locations with uncertainty information and reduces to the generalized PSR in special cases. In stochastic gradient descent (SGD), the flexibility of Bayesian PSR allows the reuse of observations in previous steps, which accelerates the optimization process. Furthermore, the accessibility to the posterior uncertainty, along with our proposed notion of gradient confident region (GradCoRe), enables us to minimize the observation costs in each SGD step. Our numerical experiments show that the VQE optimization with Bayesian PSR and GradCoRe significantly accelerates SGD and outperforms the state-of-the-art methods, including sequential minimal optimization.
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