优化模拟量子模拟的量子编码：通过动力学代数可达性
Optimizing quantum encodings for analog simulation through dynamical algebra reachability
- Laboratoire de Physique Subatomique et de Cosmologie, CNRS/IN2P3/UGA（亚原子物理与宇宙学实验室，法国国家科学研究中心/法国国家核子与粒子物理研究所/格勒诺布尔阿尔卑斯大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一个与几何无关的框架，通过黎曼梯度下降优化目标哈密顿量的酉表示，以增强模拟量子编码的代数可达性，并在里德伯原子处理器上验证其能显著改善氘核模拟的保真度与几何鲁棒性。
AI中文摘要：
模拟量子计算机提供对连续多体动力学的直接访问，但其原生控制哈密顿量仅生成受限的算子空间。因此，它们再现目标哈密顿量动力学的保真度不仅取决于谱一致性，还取决于物理控制是否实际能生成所需的演化。我们引入了一个与几何无关的框架，用于诊断和优化目标哈密顿量$H$生成的谱代数与由设备独立可调控制哈密顿量和固定初始态生成的Krylov型算子空间之间的这种兼容性。编码问题可以表述为目标哈密顿量酉轨道上的优化。我们使用$U(d)$上的黎曼梯度下降最大化一个平滑子空间重叠泛函，从而选择一个谱等价表示，其目标代数与原生控制更好地对齐。我们将此框架应用于在里德伯原子模拟处理器上编码的氘核哈密顿量。对于小系统尺寸，标准二进制编码与该空间强烈错位，而主角度优化显著提高了编码的代数兼容性。此外，使用单个与几何无关的优化编码显著降低了态制备保真度对原子几何的敏感性。这些结果确立了代数可达性作为模拟编码设计的有用预处理标准：它在设备特定几何和脉冲优化之前识别表示级不兼容性，而代数级与态级可达性之间的区别则阐明了何时需要完整编码优化以及何时几何依赖的控制资源可以补偿不完整的代数对齐。
英文摘要：
Analog quantum computers provides direct access to continuous many-body dynamics, but their native control Hamiltonians generate only a restricted operator space. Consequently, the fidelity with which they can reproduce a target Hamiltonian's dynamics depends not only on spectral agreement but on whether the physical controls can actually generate the required evolution. We introduce a geometry-independent framework for diagnosing and optimizing this compatibility between the spectral algebra generated by a target Hamiltonian $H$ and a Krylov-type operator space generated from the device's independently tunable control Hamiltonians and a fixed initial state. The encoding problem can be formulated as an optimization over the unitary orbit of the target Hamiltonian. We maximize a smooth subspace-overlap functional using Riemannian gradient descent on $U(d)$, thereby selecting a spectrally equivalent representation whose target algebra is better aligned with the native controls. We apply this framework to the deuteron Hamiltonian encoded on a Rydberg-atom analog processor. The standard binary encoding is strongly misaligned with this space for small system sizes, while principal-angle optimization substantially improves the algebraic compatibility of the encoding. Moreover, using a single geometry-independent optimized encoding substantially reduces the sensitivity of state-preparation fidelity to the atomic geometry. These results establish algebraic reachability as a useful preprocessing criterion for analog encoding design: it identifies representation-level incompatibilities before device-specific geometry and pulse optimization, while the distinction between algebra-level and state-level reachability clarifies when full encoding optimization is necessary and when geometry-dependent control resources can compensate for incomplete algebraic alignment.
