嵌入簇态疤痕的连续局域监测下的非破坏性滤波

中文摘要 AI 辅助

在多体谱中识别一个低纠缠本征态并在测量过程中保持它，是两项不同的任务。我们构造了一个显式的局域环哈密顿量，其具有精确的簇态本征向量，并研究对其稳定子缺陷的连续监测。对于任意混合输入，条件簇保真度等于初始目标权重除以无观测点击概率。正缺陷算子能隙给出了有限时间界限，该界限适用于非对易哈密顿动力学、非正规有效生成元和不完美探测。在固定总监测速率下，保证指数随系统尺寸倒数下降；高条件保真度并不能消除由初始重叠设定的制备成本。对多达十一个量子比特的精确对角化提供了在混沌谱背景中簇态离群值的有限尺寸证据。独立的矩阵和轨迹计算验证了动力学以及一个保守的相干误差界限。该构造专门化了已有的疤痕嵌入和非破坏性验证框架，并明确了测量假设、有限时间保证和资源限制。

英文摘要

Identifying a low-entanglement eigenstate inside a many-body spectrum and preserving it during measurement are distinct tasks. We construct an explicit local ring Hamiltonian with an exact cluster-state eigenvector and study continuous monitoring of its stabilizer defects. For arbitrary mixed inputs, the conditional cluster fidelity is the initial target weight divided by the no-observed-click probability. A positive defect-operator gap gives finite-time bounds that hold for noncommuting Hamiltonian dynamics, nonnormal effective generators and imperfect detection. At fixed total monitoring rate, the guaranteed exponent falls inversely with system size; high conditional fidelity does not remove the preparation cost set by the initial overlap. Exact diagonalization up to eleven qubits gives finite-size evidence for a cluster-state outlier in a chaotic spectral background. Independent matrix and trajectory calculations verify the dynamics and a conservative coherent-error bound. This construction specializes established scar embedding and nondemolition verification frameworks, with explicit measurement assumptions, finite-time guarantees and resource limitations.

发表机构

• School of Physics and Electronic Engineering, Shanxi University（山西大学物理电子工程学院）
• Collaborative Innovation Center of Extreme Optics, Shanxi University（山西大学极端光学协同创新中心）
• Department of Physics, University of Science and Technology of China（中国科学技术大学物理系）
• School of Instrument Science and Opto-Electronics Engineering, Beijing Information Science and Technology University（北京信息科技大学仪器科学与光电工程学院）
• School of Physics, Beihang University（北京航空航天大学物理学院）
• School of Applied Science, Beijing Information Science and Technology University（北京信息科技大学应用科学学院）
• School of Automation (School of Artificial Intelligence), Beijing Information Science and Technology University（北京信息科技大学自动化学院（人工智能学院））
• School of Space and Earth Sciences, Beihang University（北京航空航天大学空间与地球科学学院）

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