无假设哈密顿量的最优原位学习
Optimal Ansatz-free Hamiltonian Learning In Situ
- Department of Information Engineering, The Chinese University of Hong Kong（香港中文大学信息工程系）
- John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保罗森工程与应用科学学院）
- California Institute of Technology（加州理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出一种无需控制、无需辅助比特的算法，仅用泡利乘积态制备和测量，以最优总演化时间学习无假设哈密顿量，适用于近中期量子实验。
AI中文摘要：
描述控制量子系统的哈密顿量特征，是量子设备校准、信号传感和纠错的基本子程序。近期工作提出了协议，通过实时演化实现无假设哈密顿量的最优海森堡极限学习，无需完全指定相互作用结构。然而，这些协议依赖于带有交错探测和控制的深电路以及极短的时间分辨率，使其难以在近中期原位量子实验中实现。本文提出一种计算高效、无需控制、无需辅助比特的算法，仅使用泡利乘积态制备和测量，在总演化时间 $\Theta(\frac{\Lambda}{\epsilon^2}\log(\frac{\Lambda}{\epsilon}))$ 内学习无假设哈密顿量 $H$（满足 $||H||\leq\Lambda$）。该算法的演化时间成本对于任何无控制协议是最优的，因为我们进一步证明了 $\Omega(\frac{\Lambda}{\epsilon^2}\log(\frac{\Lambda}{\epsilon}))$ 的下界。技术上，我们的方法引入了一个随机采样框架，结合了带限核时间采样和用于哈密顿量结构学习的位移筛。特征探测时间分辨率仅依赖于 $\Lambda$ 而非 $\varepsilon$，这使得我们的协议在传感和校准的高精度场景中特别有吸引力。我们还表明，当哈密顿量在校准后是局域的时，该算法在存在状态制备和测量（SPAM）噪声的情况下保持相同的渐近总演化时间。我们的结果展示了实验友好型哈密顿量学习的基本成本，并为近中期量子平台的严格原位表征提供了实用途径。
英文摘要：
Characterizing the features of a Hamiltonian that governs a quantum system serves as a fundamental subroutine of quantum device calibration, signal sensing, and error correction. Recent works have proposed protocols achieving the optimal Heisenberg-limited scaling learning ansatz-free Hamiltonians from their real-time evolutions without fully specifying interaction structures. However, these protocols rely on both deep circuits with interleaving probes and control, and extremely short time resolution, making them difficult to implement on near- and intermediate-term in situ quantum experiments. In this work, we propose a computationally efficient, control-free, and ancilla-free algorithm that uses only Pauli product state preparation and measurement, and learns an ansatz-free Hamiltonian $H$ with $||H||\leqΛ$ in total evolution time of $Θ(\fracΛ{ε^2}\log(\fracΛε))$. The evolution time cost of our algorithm is optimal for any control-free protocols as we further prove a lower bound of $Ω(\fracΛ{ε^2}\log(\fracΛε))$. Technically, our method introduces a randomized-sampling framework that combines band-limited kernel-based time sampling with a displacement sieve for Hamiltonian structure learning. The characteristic probe time resolution depends only on $Λ$ instead of $\varepsilon$, which makes our protocol especially appealing in the high-precision regime for sensing and calibration applications. We also show that the algorithm maintains the same asymptotic total evolution time in the presence of state-preparation-and-measurement (SPAM) noise when the Hamiltonian is local after calibration. Our results demonstrate the fundamental cost of experimentally friendly Hamiltonian learning and provide a practical route to rigorous in situ characterization of near-term quantum platforms.
