发表机构
University of British Columbia; Stewart Blusson Quantum Matter Institute; Jagiellonian University; Los Alamos National Laboratory; IBM Research; European Space Agency (ESA/ESRIN); Johannes Kepler University; Mark Kac Center for Complex Systems Research（英属哥伦比亚大学; 斯图尔特·布卢森量子物质研究所; 雅盖隆大学; 洛斯阿拉莫斯国家实验室; IBM研究院; 欧洲空间局（欧洲空间局/欧洲空间研究与技术中心）; 约翰内斯·开普勒大学; 马克·卡茨复杂系统研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文扩展量子高斯过程（QGP）框架至非幺数量子信道，提出经验贝叶斯启发式方法优化核函数，通过数值模拟和噪声量子计算机实验验证其在信道观测预测及态制备贝叶斯优化中的有效性。
AI 中文摘要
给定一组输入态，我们考虑仅使用有限次测量来预测未知量子演化输出处泡利可观测量的期望值这一任务。近期，量子高斯过程（QGP）回归已被引入，用于针对各类幺正演化完成该任务。本文将QGP框架扩展至超越幺正动力学的范畴，具体而言，我们证明了信道输出收敛于QGP，并在量子信道的均匀（勒贝格测度）先验下推导了对应的闭式核函数。然而，该核函数的维度因子决定了所需的观测精度：当信道与可观测量被限制在小子系统中时，该精度可被控制；但当子系统随系统规模呈指数增长时，指数抑制会导致无法学习。由于勒贝格先验在诸多应用中过于宽泛，我们提出一种经验贝叶斯启发式方法，在保留核函数的态-重叠相关结构的同时，用可学习的尺度参数替代维度因子。在最多64量子比特的数值模拟中，采用勒贝格核的信道QGP回归对局部信道展现出强归纳偏置，可实现可靠外推；对于全局64量子比特信道，重标后的核函数恢复了可学习性，预测结果随采样预算（shot budget）的增加而系统地提升。来自噪声量子计算机的结果进一步证明了QGP回归在实验条件下的鲁棒性。除回归任务外，我们还验证了QGP作为贝叶斯优化替代模型，在噪声XXZ动力学下的态制备任务中的有效性。
英文摘要
Given a set of input states, we consider the task of predicting the expectation value of a Pauli observable at the output of an unknown quantum evolution, using only a limited number of measurements. Recently, quantum Gaussian process (QGP) regression was introduced for this task across various classes of unitary evolution. Here, we extend the QGP framework beyond unitary dynamics. In particular, we prove convergence of the channel's outputs to a QGP and derive the associated closed-form kernel under a uniform (Lebesgue measure) prior over quantum channels. The kernel's dimensional factor, however, dictates the required observation precision. While manageable when the channel and observable are restricted to small subsystems, exponential suppression precludes learning when the subsystem grows extensively with the system size. Since the Lebesgue prior is overly broad for many applications, we propose an empirical Bayes heuristic that replaces the dimensional factor with a learnable scale parameter while retaining the kernel's state-overlap correlation structure. In numerical simulations of up to 64 qubits, channel QGP regression with the Lebesgue kernel exhibits a strong inductive bias for local channels, enabling faithful extrapolation. For global 64-qubit channels, the rescaled kernel restores learnability, with predictions improving systematically with the shot budget. Results from a noisy quantum computer further demonstrate the robustness of QGP regression under experimental conditions. Beyond regression, we validate QGPs as Bayesian-optimization surrogates for state preparation under noisy XXZ dynamics.
Comments14 + 7 pages, 5 + 2 figures
