发表机构
University of Houston; Miami University（休斯顿大学; 迈阿密大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明容错表面码存储器的执行转录在特定条件下不泄露逻辑输入，但各向异性导致Z距离决定泄露，实验验证了理论界限。
AI 中文摘要
容错量子计算机在遥测流背后运行，该遥测流记录综合征、解码器动作、重置和时序，与答案分开记录。这能否揭示逻辑输入？对于固定调度为T=Θ(d)轮的d距离旋转表面码存储器，在三个既定假设（扇区标量诚实骨干、转录局部性、Kotecky-Preiss小性）下，从逻辑量子比特到转录的信道在金刚石范数下与忽略输入的信道e^{-Θ(d)}接近。这种陈述通常可由可纠正性-隐私对偶性得出。各向异性则不然。每个逻辑轴承担其自身陪集的距离，因此在振幅阻尼下，计算基标签由码的Z距离d_Z≥d_min决定，而非码距离。两个量子距离为1的码使这一差距具体化。相位翻转码的X综合征转录在未观测阻尼下完全独立于输入，而重复码在一阶泄露。一个匹配的反向识别出确实暴露它的记录，其中包括晶格手术奇偶校验读出。在156量子比特超导处理器上，我们的充分证书相差21.5倍，因此该定理不能在此处引用。直接测量时，d_Z=1存储器的记录在随机、标签平衡采集下以总变差≥0.927识别其输入。固定码并改变阻尼暴露重现了无参数定律，指数为0.85±0.03，而预测值为0.86。随机编码以零双量子比特门代价将统计量恢复到下限。容错并不授予转录隐私。它将其重新定位，且仅定位到逻辑状态，而非电路身份。
英文摘要
A fault-tolerant quantum computer runs behind a telemetry stream logging syndromes, decoder actions, resets and timing separately from the answer. Can it reveal the logical input? For a distance-$d$ rotated surface-code memory on a fixed schedule of $T=Θ(d)$ rounds, under three stated hypotheses (sector-scalar honest backbone, transcript locality, Kotecky-Preiss smallness), the channel from logical qubit to transcript is $e^{-Θ(d)}$-close in diamond norm to one that ignores the input. A statement of this kind follows generically from correctability-privacy duality. Anisotropy does not. Each logical axis pays the distance of its own coset, so under amplitude damping the computational-basis label is governed by the code's $Z$-distance $d_Z\ge d_{\min}$ and not by the code distance. Two codes of quantum distance $1$ make the gap concrete. A phase-flip code's $X$-syndrome transcript is exactly input-independent under unobserved damping, while a repetition code leaks at first order. A matched converse identifies the records that do expose it, among them a lattice-surgery parity readout. On a 156-qubit superconducting processor our sufficient certificate misses by $21.5\times$, so the theorem cannot be invoked there. Measured directly, a $d_Z=1$ memory's record identifies its input with total variation $\ge 0.927$ under randomised, label-balanced acquisition. Holding the code fixed and varying the damping exposure reproduces the parameter-free law, with exponent $0.85\pm0.03$ against a predicted $0.86$. Randomized encoding returns the statistic to the floor at no two-qubit-gate cost. Fault tolerance does not grant transcript privacy. It relocates it, and only to the logical state, not to the circuit's identity.
Comments138 pages including appendices, 12 figures, 22 tables
