多对数深度量子热模拟：基于局域恢复通道
Polylog-depth Quantum Thermal Simulation via Local Recovery Channels
- University of Osaka（大阪大学）
- University of Tokyo（东京大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出在任意固定空间维度下，利用局域Petz恢复映射和经典参考哈密顿量，以多对数深度电路制备非对易局域哈密顿量的量子热态，并给出充分条件，建立了平衡局域性与量子算法效率的关联。
AI中文摘要：
我们建立了在任意固定空间维度下，以多对数电路深度制备非对易局域哈密顿量量子热态的充分条件。我们的条件将吉布斯态约化密度矩阵有效相互作用的局域性与稳定性界，与定量高温条件及对粗糙经典参考哈密顿量的访问相结合。当这些参考哈密顿量可局域生成时，经典预处理成本为 $N^{1+o(1)}$（$N$ 为格点数目），全局精度为逆多项式。我们利用空间局域的 Petz 恢复映射构造制备电路。由微观哈密顿量导出的量子修正使得恢复过程精确，而经典参考保持粗糙。预处理后，所得电路使用 $N\operatorname{polylog}(N/\varepsilon)$ 个门和量子比特制备规范纯化态，其中 $\varepsilon$ 为制备误差。这些结果将两个基本问题联系起来：热平衡中关联如何组织，以及量子力学允许的操作能多高效地实现相应状态。通过将静态平衡结构转化为显式制备电路，我们的工作赋予平衡局域性以建设性的计算解释，并使其在量子算法设计中发挥基于物理的实质作用。
英文摘要：
We establish sufficient conditions for preparing quantum thermal states of noncommuting local Hamiltonians with polylogarithmic circuit depth in arbitrary fixed spatial dimension. Our conditions combine locality and stability bounds on the effective interactions of reduced density matrices of a Gibbs state with a quantitative high-temperature condition and access to coarse classical reference Hamiltonians. When these references can be generated locally, the classical preprocessing cost is $N^{1+o(1)}$ for $N$ sites at inverse-polynomial global accuracy. We construct the preparation circuit from spatially localized Petz recovery maps. Quantum corrections derived from the microscopic Hamiltonian enable accurate recovery while the classical references remain coarse. After preprocessing, the resulting circuit prepares the canonical purification using $N\operatorname{polylog}(N/\varepsilon)$ gates and qubits, where $\varepsilon$ is the preparation error. These results link two fundamental questions: how correlations are organized in thermal equilibrium, and how efficiently the corresponding states can be realized through operations allowed by quantum mechanics. By translating static equilibrium structure into explicit preparation circuits, they give equilibrium locality a constructive computational interpretation and a physically grounded role in quantum algorithm design.
