发表机构
Cleveland Clinic Research（克利夫兰诊所研究）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出谱核心-尾部架构（SCTA）框架，用于局部认证的Gibbs态制备，通过分离核心制备、尾部实现和建模误差，并利用Schrieffer-Wolff约化处理形变，数值验证了误差的二次抑制及变分拟设的实用性。
AI 中文摘要
制备量子Gibbs态需要同时再现其热分布和相关的多体本征空间。在本工作中，我们将谱核心-尾部架构（SCTA）形式化为一个框架，该框架包含一个结构化的热核心、一个几何特征化的酉尾部，以及一个精确的残差项，用于度量剩余的核心-框架哈密顿量失配。我们推导出一个局域Gibbs态误差界，将核心制备、尾部实现和建模误差分离开来。当建模贡献的Kubo-Mori响应满足壳层可加性条件且相关局域数据保持均匀时，该贡献是体积均匀的。然后，我们重点介绍三类锚定哈密顿量类，它们允许精确的核心-尾部构造且残差为零。对于精确锚定的小形变，我们采用Schrieffer-Wolff约化程序来构造一个修正的核心-尾部对，该对按阶形式化地消除形变。在均匀局域性和可解性假设下，我们证明一阶约化产生的残差保持有界且与形变强度呈二次关系。此外，我们在变形的图-稳定子哈密顿量上数值测试了一阶约化。数值结果表明，在微扰区域中，哈密顿量级失配和局域Gibbs态误差均近似呈二次抑制。我们还发现，所构造的修正电路结构在微扰控制之外作为变分拟设仍然有用，通常优于裸态和规定的一阶态。
英文摘要
Preparing a quantum Gibbs state requires reproducing both its thermal distribution and the associated many-body eigenspaces. In this work, we formalize the spectral core-tail architecture (SCTA) as a framework comprising a structured thermal core, a geometrically characterized unitary tail, and an exact residual measuring the remaining core-frame Hamiltonian mismatch. We derive a local Gibbs-state error bound separating core-preparation, tail-implementation, and modeling errors. The modeling contribution is volume uniform when its Kubo-Mori response meets the shell summability condition and the relevant local data remain uniform. We then highlight three anchor Hamiltonian classes which admit exact core-tail constructions with zero residuals. For small deformations of an exact anchor, we employ a Schrieffer-Wolff reduction procedure to construct a corrected core-tail pair that formally removes the deformation order by order. Under uniform locality and solvability assumptions, we show that the first-order reduction yields a residual that remains bounded and is quadratic in the deformation strength. Furthermore, we numerically test the first-order reduction on deformed graph-stabilizer Hamiltonians. The numerical results show approximately quadratic suppression of both the Hamiltonian-level mismatch and the local Gibbs-state error in the perturbative regime. We also find that the constructed correction circuit structure remains useful as a variational ansatz beyond perturbative control, often improving on both the bare and prescribed first-order states.
Comments23 pages + supplemental material
