无需预先知道哈密顿量结构，即可高效学习任意量子多体系统演化规律。
Learning the structure of any Hamiltonian from minimal assumptions
- 利用伪乔伊态作为核心工具，不依赖局部性假设即可推断哈密顿量结构。
- 在时间反演条件下，仅需约 $\widetilde{\mathcal{O}}(m/ε)$ 总演化时间即可获得 $ε$ 精度的古典描述。
- 适用于无先验知识的通用量子系统识别，适合量子信息与量子控制研究者。
我们研究从黑箱查询其时间演化 $e^{-\mathrm{i} H t}$ 来学习未知量子多体哈密顿量 $H$ 的问题。以往方法要么对 $H$ 的相互作用结构或局域性施加假设，要么需要指数级后处理计算。本文提出算法，可学习任意 $n$-量子比特哈密顿量，无需事先知晓其项或限制为局域相互作用。只要项数 $m$ 在系统规模 $n$ 下多项式有界，算法即高效。我们考虑两种演化控制模型：第一种支持时间反演（$t < 0$），可在总演化时间 $\widetilde{\mathcal{O}}(m/ε)$ 内输出 $ε$-精度的古典描述；第二种仅允许正向演化，所需时间约为 $\widetilde{\mathcal{O}}(\|H\|^3/ε^4)$。核心是近期提出的伪乔伊态 $H$，我们进一步展示了如何用它学习 $H$ 的傅里叶谱、实现近海森堡极限标度，并在更受限模型下准备该态。
原文摘要 · Abstract (English)
We study the problem of learning an unknown quantum many-body Hamiltonian $H$ from black-box queries to its time evolution $e^{-\mathrm{i} H t}$. Prior proposals for solving this task either impose some assumptions on $H$, such as its interaction structure or locality, or otherwise use an exponential amount of computational postprocessing. In this paper, we present algorithms to learn any $n$-qubit Hamiltonian, which do not need to know the Hamiltonian terms in advance, nor are they restricted to local interactions. Our algorithms are efficient as long as the number of terms $m$ is polynomially bounded in the system size $n$. We consider two models of control over the time evolution:~the first has access to time reversal ($t < 0$), enabling an algorithm that outputs an $ε$-accurate classical description of $H$ after querying its dynamics for a total of $\widetilde{\mathcal{O}}(m/ε)$ evolution time. The second access model is more conventional, allowing only forward-time evolutions;~our algorithm requires $\widetilde{\mathcal{O}}(\|H\|^3/ε^4)$ evolution time in this setting. Central to our results is the recently introduced concept of a pseudo-Choi state of $H$. We extend the utility of this learning resource by showing how to use it to learn the Fourier spectrum of $H$, how to achieve nearly Heisenberg-limited scaling with it, and how to prepare it even under our more restricted access models.
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