AI 中文总结
该研究提出有限窗口恢复层级作为局域控制基准，通过局域变分恢复方法，在无序驱动伊辛Floquet链等场景中验证了浅层控制可恢复异地量子信息，实现了高于经典基准的修复性能。
AI 中文摘要
当初始存储在局域量子比特中的量子信息消失时，它未必会丢失，可能已转移到邻近的自由度中，或变得难以被浅层局域控制访问。我们引入有限窗口可恢复性作为一种可操作的信道基准，以区分上述两种可能性。该基准比较了从目标位点的最优恢复、有限窗口上有界深度解码器的恢复，以及该窗口的无限制最优恢复。其可操作组件为局域变分恢复，它利用局域态制备、窗口局域控制和目标量子比特泡利读出，以验证目标之外可恢复的存储器，并量化浅层控制可获取的同窗口优势的比例。在无序驱动伊辛Floquet链中，五位点窗口上的深度6解码器在交叉区域实现了$Q^{\text{opt}}_0<Q^{\text{shallow}}_2<Q^{\text{opt}}_2$，且对于大多数无序实现，存在正的验证增益，浅层可访问分数也较高。该信号与目标位点持续性及重构相干信息增量不同。当任务嵌入使用独立张量网络后端的更长开放链时，半径2的正增益仍持续存在。基于该层级，我们测试了载体删除任务，其中动力学后原始目标寄存器被重置。深度8解码器从半径3的周围晕环修复输入，保留的平均保真度$F_{\text{avg}}=0.758$，高于单量子比特经典基准$2/3$，且优于最优的1、2、3位点晕环子窗口反事实情况。这些结果确立了有限窗口恢复作为用于异地量子存储器的局域控制基准，可诊断局域量子信息保留的位置，以及有界深度控制是否能将其重新聚焦。
英文摘要
When quantum information initially stored in a local qubit disappears, it need not be lost: it may have moved into nearby degrees of freedom or become inaccessible to shallow local control. We introduce finite-window recoverability as an operational channel benchmark that separates these possibilities. It compares optimal recovery from the target site, recovery by a bounded-depth decoder on a finite window, and the unrestricted optimum for that window. Its operational component, local variational recovery, uses local state preparation, window-local control, and target-qubit Pauli readout to certify recoverable memory beyond the target and quantify how much of the same-window advantage is accessible to shallow control. In a disordered kicked-Ising Floquet chain, a depth-6 decoder on a five-site window realizes $Q^{\mathrm{opt}}_0<Q^{\mathrm{shallow}}_2<Q^{\mathrm{opt}}_2$ across the crossover regime, with positive certified gain for most disorder realizations and substantial shallow-accessibility fractions. The signal differs from target-site persistence and reconstructed coherent-information increments. Positive radius-2 gain also persists when the task is embedded in longer open chains using an independent tensor-network backend. Guided by this hierarchy, we test a carrier-deletion task in which the original target register is reset after the dynamics. A depth-8 decoder repairs the input from a radius-3 surrounding halo with held-out median $F_{\mathrm{avg}}=0.758$, above the single-qubit classical benchmark $2/3$, and outperforms optimal one-, two-, and three-site halo-subwindow counterfactuals. These results establish finite-window recovery as a local-control benchmark for off-site quantum memory, diagnosing both where local quantum information remains and whether bounded-depth control can refocus it.
Comments23 pages, 16 figures; includes Methods and appendices
