论文标题
实用的黑匣子汉密尔顿学习
Practical Black Box Hamiltonian Learning
论文作者
论文摘要
我们研究了量子多体系统的哈密顿量的参数的问题，鉴于对系统的访问有限。在这项工作中，我们基于最近通过衍生估计进行哈密顿学习的方法。我们提出了一项协议，以改善先前工作的缩放依赖性，尤其是在与汉密尔顿的结构有关的参数方面（例如，其位置$ k $）。此外，通过在协议的性能上得出精确的界限，我们能够在我们的学习协议中为高参数的理论上最佳设置提供精确的数值处方，例如最大进化时间（当单位动力学学习时）或最低温度（使用GIBBS状态学习时）。多亏了这些改进，我们的协议对于大型问题很实际：我们通过对80 QUIT系统的协议进行数值模拟来证明这一点。
We study the problem of learning the parameters for the Hamiltonian of a quantum many-body system, given limited access to the system. In this work, we build upon recent approaches to Hamiltonian learning via derivative estimation. We propose a protocol that improves the scaling dependence of prior works, particularly with respect to parameters relating to the structure of the Hamiltonian (e.g., its locality $k$). Furthermore, by deriving exact bounds on the performance of our protocol, we are able to provide a precise numerical prescription for theoretically optimal settings of hyperparameters in our learning protocol, such as the maximum evolution time (when learning with unitary dynamics) or minimum temperature (when learning with Gibbs states). Thanks to these improvements, our protocol is practical for large problems: we demonstrate this with a numerical simulation of our protocol on an 80-qubit system.
