标题： 哈密顿量的实时演化结构学习 显示英文标题

标题： Structure learning of Hamiltonians from real-time evolution

摘要： 我们研究从实时演化中学习哈密顿量结构的问题：给定能够对未知局部哈密顿量$H = \sum_{a = 1}^m \lambda_a E_a$在$n$个量子比特上应用$e^{-\mathrm{i} Ht}$的能力，目标是恢复$H$。 在假设相互作用项$E_a$已知的情况下，这个问题已经得到了很好的理解，只有相互作用强度$\lambda_a$是未知的。 但是，在没有先验知识的情况下，我们能多高效地学习一个局部哈密顿量呢？ 我们提出了一种新的、通用的哈密顿量学习方法，不仅解决了具有挑战性的结构学习变体，还解决了该领域中的其他开放问题，同时实现了海森堡极限的标度标准。 特别是，我们的算法在总演化时间$O(\log (n)/\varepsilon)$内将哈密顿量恢复到$\varepsilon$的误差，并具有以下吸引人的特性：(1) 它不需要知道哈密顿量的项；(2) 它超越了短程设置，在任何哈密顿量$H$中有效，其中与一个量子比特相互作用的项的和具有有界范数；(3) 它按照$H$在常数时间$t$增量中演化，从而实现常数时间分辨率。作为应用，我们还可以学习表现出幂律衰减的哈密顿量，达到精度$\varepsilon$，总演化时间超过标准极限$1/\varepsilon^2$。 显示英文摘要

摘要： We study the problem of Hamiltonian structure learning from real-time evolution: given the ability to apply $e^{-\mathrm{i} Ht}$ for an unknown local Hamiltonian $H = \sum_{a = 1}^m \lambda_a E_a$ on $n$ qubits, the goal is to recover $H$. This problem is already well-understood under the assumption that the interaction terms, $E_a$, are given, and only the interaction strengths, $\lambda_a$, are unknown. But how efficiently can we learn a local Hamiltonian without prior knowledge of its interaction structure? We present a new, general approach to Hamiltonian learning that not only solves the challenging structure learning variant, but also resolves other open questions in the area, all while achieving the gold standard of Heisenberg-limited scaling. In particular, our algorithm recovers the Hamiltonian to $\varepsilon$ error with total evolution time $O(\log (n)/\varepsilon)$, and has the following appealing properties: (1) it does not need to know the Hamiltonian terms; (2) it works beyond the short-range setting, extending to any Hamiltonian $H$ where the sum of terms interacting with a qubit has bounded norm; (3) it evolves according to $H$ in constant time $t$ increments, thus achieving constant time resolution. As an application, we can also learn Hamiltonians exhibiting power-law decay up to accuracy $\varepsilon$ with total evolution time beating the standard limit of $1/\varepsilon^2$.