发表机构
Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL); Center for Quantum Science and Engineering, EPFL（洛桑联邦理工学院物理研究所; 洛桑联邦理工学院量子科学与工程中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对含噪声能量下玻尔兹曼分布采样的偏差问题，提出泊松乘积估计器，将其用于无梯度优化变分量子电路，成功得到H₃⁺基态能量并绘制变分能量 landscape。
AI 中文摘要
从玻尔兹曼分布采样是计算物理学的核心任务，但当能量仅能通过随机估计获取时，例如机器学习分子势、变分蒙特卡洛或量子计算机场景，这一任务极具挑战性，因为含噪声的能量会使采样分布产生偏差。Ceperley和Dewing的惩罚法可修正该问题，但需知晓噪声方差，且当噪声方差较大时会变得难以处理。我们提出泊松乘积估计器，这是一种无偏、非负的玻尔兹曼权重估计器，仅需能量估计值的上界，且在高噪声下仍保持高效。将其用于无梯度优化变分量子电路，我们在最小基组下成功得到H₃⁺的基态能量，并且通过采样而非跟踪单一轨迹，还绘制了变分能量 landscape。
英文摘要
Sampling from the Boltzmann distribution is central to computational physics, yet hard when the energy is known only through a stochastic estimate, such as with machine-learned molecular potentials, in variational Monte Carlo, or on quantum computers, because a noisy energy biases the sampled distribution. The penalty method of Ceperley and Dewing corrects this but requires the noise variance and becomes intractable when it is large. We introduce the Poisson product estimator, an unbiased, non-negative estimator of the Boltzmann weight that only needs an upper bound on the energy estimator and remains efficient at high noise. Using it to optimize a variational quantum circuit gradient-free, we recover the $H_3^+$ ground-state energy in a minimal basis and, by sampling rather than following a single trajectory, also map the variational energy landscape.
Comments9 pages, 3 figures
