论文标题
通过海森堡限制缩放来学习多体汉密尔顿人
Learning many-body Hamiltonians with Heisenberg-limited scaling
论文作者
论文摘要
从动力学中学习多体哈密顿量是物理学中的基本问题。在这项工作中，我们提出了第一种实现海森堡限制的算法，以学习互动的$ n $ qubit当地汉密尔顿人。在总进化时间为$ \ MATHCAL {O}（ε^{ - 1}）$之后，提出的算法可以有效地估计$ n $ qubit Hamiltonian中的任何参数至$ε$ -REROR，具有很高的可能性。所提出的算法对状态准备和测量误差非常强大，不需要特征状态或热状态，并且仅使用$ \ mathrm {polylog}（ε^{ - 1}）$实验。相比之下，最好的先前算法，例如使用基于梯度的优化或多项式插值的最新作品，需要$ \ Mathcal {O}（O}（ε^{ - 2}）$和$ \ MATHCAL {O}（ε^{ - 2}）$实验的总进化时间。我们的算法使用量子模拟的想法将未知的$ n $ qubit Hamiltonian $ h $与非相互作用的补丁分发，并使用量子增强的分界线和相关方法来学习$ h $。我们证明了一个匹配的下限，以建立算法的渐近优化性。
Learning a many-body Hamiltonian from its dynamics is a fundamental problem in physics. In this work, we propose the first algorithm to achieve the Heisenberg limit for learning an interacting $N$-qubit local Hamiltonian. After a total evolution time of $\mathcal{O}(ε^{-1})$, the proposed algorithm can efficiently estimate any parameter in the $N$-qubit Hamiltonian to $ε$-error with high probability. The proposed algorithm is robust against state preparation and measurement error, does not require eigenstates or thermal states, and only uses $\mathrm{polylog}(ε^{-1})$ experiments. In contrast, the best previous algorithms, such as recent works using gradient-based optimization or polynomial interpolation, require a total evolution time of $\mathcal{O}(ε^{-2})$ and $\mathcal{O}(ε^{-2})$ experiments. Our algorithm uses ideas from quantum simulation to decouple the unknown $N$-qubit Hamiltonian $H$ into noninteracting patches, and learns $H$ using a quantum-enhanced divide-and-conquer approach. We prove a matching lower bound to establish the asymptotic optimality of our algorithm.
