涌现预热对称性用于可扩展哈密顿量学习
Emergent Prethermal Symmetries for Scalable Hamiltonian Learning
- Korea Advanced Institute of Science and Technology（韩国科学技术院）
- California Institute of Technology（加州理工学院）
- Harvard University（哈佛大学）
- Duke University（杜克大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种仅用静态单量子比特场即可在海森堡极限下学习几何局域多体哈密顿量的协议，通过涌现预热对称性抑制热化，实现信息论最优精度，无需快速或可信多量子比特控制。
AI中文摘要：
在海森堡极限下学习相互作用的量子多体哈密顿量，通常需要控制手段在约 $1/\varepsilon$ 的演化时间内保留局部信息，以达到 $\varepsilon$ 精度。为实现这一目标，现有协议往往依赖可信的多量子比特操作或日益快速的脉冲控制，但当门操作涉及未知的多量子比特相互作用或具有有限持续时间时，这会形成精度障碍。我们证明，对于几何局域哈密顿量，这两种资源均非必需。我们的协议仅施加静态单量子比特场，其强度与系统尺寸无关，并随 $1/\varepsilon$ 呈多对数增长。这些场产生涌现的预热对称性，在整个学习实验过程中抑制热化，同时保留信息丰富的对称性保持动力学。在 $n$ 个量子比特的 $d$ 维晶格上，该协议能够以 $\varepsilon$ 精度学习每个系数，失败概率至多为 $\delta$，总演化时间为 $\mathcal{O}(\log^d(1/\varepsilon)\log^2(n/\delta)/\varepsilon)$。因此，我们的学习协议利用乘积态制备、单量子比特测量和非自适应实验，实现了信息论最优的 $1/\varepsilon$ 依赖（至多相差多对数因子）。更广泛地，我们的结果确立了涌现预热对称性作为量子学习的资源，为在缺乏快速或可信多量子比特控制的情况下对多体系统进行海森堡极限表征开辟了途径。
英文摘要：
Learning an interacting many-body Hamiltonian at the Heisenberg limit generally requires control that preserves local information for evolution times of order $1/\varepsilon$ to attain $\varepsilon$ precision. To achieve this, existing protocols often rely on trusted many-qubit operations or increasingly rapid control pulses, creating a precision barrier when gates involve unknown multi-qubit interaction or have finite duration. We show that neither resource is necessary for geometrically local Hamiltonians. Our protocol applies only static single-qubit fields, whose strength is independent of system size and grows polylogarithmically with $1/\varepsilon$. These fields generate emergent prethermal symmetries that suppress thermalization for the entire learning experiment while retaining informative symmetry-preserving dynamics. On a $d$-dimensional lattice of $n$ qubits, this enables learning every coefficient to accuracy $\varepsilon$, with failure probability at most $δ$, using total evolution time $\mathcal{O}(\log^d(1/\varepsilon)\log^2(n/δ)/\varepsilon).$ Thus, our learning protocol attains the information-theoretically optimal \(1/\varepsilon\) dependence up to polylogarithmic factors using product-state preparation, single-qubit measurements, and non-adaptive experiments. More broadly, our results establish emergent prethermal symmetries as a resource for quantum learning, opening a route to Heisenberg-limited characterization of many-body systems where fast or trusted many-qubit control is unavailable.
