学习宇称超选择下的局域费米子林德布拉德算符
Learning Local Fermionic Lindbladians under Parity Superselection
- University of Cambridge（剑桥大学）
- University of Tübingen（蒂宾根大学）
- University of Copenhagen（哥本哈根大学）
- Inria, Télécom Paris–LTCI, Institut Polytechnique de Paris（法国国家信息与自动化研究所，巴黎高等电信学院-通信与图像处理实验室，巴黎理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出在宇称超选择约束下，利用内部标记和配对测量学习局域费米子林德布拉德算符的方法，实现了样本高效的系数恢复与误差保证。
AI中文摘要：
宇称超选择禁止直接测量奇数马约拉纳可观测量。我们利用偶数制备和测量以及不间断的短时演化，学习m个模式上时间无关、宇称协变的k模式局域林德布拉德算符。内部标记将奇数探针转化为偶数可观测量，三个分离标记之间的配对测量校准其动力学贡献。符号费米反转恢复正则系数，而半定拟合产生有效的生成元。对于已知有界度图上的有限范围模型，在合适的标记访问和提供的加权强度界\bar\alpha下，使用\widetilde{\mathcal{O}}(\bar\alpha^2\varepsilon^{-2}\log(m/\delta))个样本实现逐项误差\varepsilon，无需外部模式或已知非零系数位置。达到金刚石范数误差\varepsilon的恢复额外花费因子m^2，与新鲜系统上短时实验的下界匹配（除对数及固定几何因子外）。在没有提供图的情况下，每个系统模式一个空闲辅助模式以及潜在的非局域配对操作，在提供的近似系数度界\mathsf d和受控弱系数尾部下，使用\widetilde{\mathcal{O}}_k(\bar\alpha^2\mathsf d^2m^{\lfloor k/2\rfloor}\varepsilon^{-2}\log(m/\delta))个样本，使每模式总绝对系数误差至多\varepsilon。所有保证以至少1-\delta的概率成立。对于几何模型，在固定时间和精度下，固定支撑偶数可观测量可以以系统规模的对数样本复杂度预测。我们还给出了有限体积和指数尾部扩展。
英文摘要：
Parity superselection forbids direct measurement of odd Majorana observables. We learn time-independent, parity-covariant, $k$-mode-local Lindbladians on $m$ modes using even preparations and measurements with uninterrupted short-time evolution. Internal markers turn odd probes into even observables, and pair measurements among three separated markers calibrate their dynamical contributions. Signed Fierz inversion recovers canonical coefficients, while semidefinite fitting yields a valid generator. For finite-range models on known bounded-degree graphs with suitable marker access and a supplied weighted-strength bound $\barα$, entrywise error $\varepsilon$ is achieved using $\widetilde{\mathcal{O}}(\barα^2\varepsilon^{-2}\log(m/δ))$ samples, without external modes or known nonzero coefficient locations. Recovery to diamond-norm error $\varepsilon$ costs an additional factor $m^2$, matching lower bounds for short-time experiments on fresh systems up to logarithmic and fixed geometric factors. Without a supplied graph, one idle ancillary mode per system mode and potentially nonlocal pair operations give total absolute coefficient error at most $\varepsilon$ per mode using $\widetilde{\mathcal{O}}_k(\barα^2\mathsf d^2m^{\lfloor k/2\rfloor}\varepsilon^{-2}\log(m/δ))$ samples, under a supplied approximate coefficient-degree bound $\mathsf d$ and controlled weak-coefficient tails. All guarantees hold with probability at least $1-δ$. For geometric models, fixed-support even observables can be predicted with logarithmic system-size sample complexity at fixed time and accuracy. We also give finite-volume and exponential-tail extensions.
