AI 中文总结
本文针对子空间量子纠错，量化了症候存储器清除的能量代价，结合码结构、噪声与症候表示分析了其下界及层级，为量子纠错的热力学负担提供了理论依据。
AI 中文摘要
量子纠错如同熵泵，将受保护量子系统中噪声诱导的不确定性转移至存储在辅助存储器的症候信息中。重复操作需要清除该存储器，这不可避免地会增加纠错的能量代价。本文针对子空间量子纠错码表征了这一贡献，并确定其如何依赖于码的联合结构、噪声以及保留症候信息的表示。从Knill-Laflamme条件出发，我们构造了一个有效症候态，其冯·诺依曼熵为维持可重复使用的症候寄存器所需的理想功设定了下界。投影式症候读出通常会产生额外的熵，我们通过测量效率量化了由此产生的差距。随后，我们聚焦于独立局域泡利噪声下的稳定器码，并分析了两种经典的症候表示层级：在抽象错误标记层级，单量子比特错误的简并性降低了经处理的恢复标记的领头阶熵；在奇偶校验层级，低权重校验在低噪声 regime 中降低了单个测量结果产生的边际熵。我们确定了与保留并单独擦除这些结果相关的额外负担，即比特级效率低下，并针对五量子比特码、Steane码、广义Shor码和旋转表面码说明了这两种代价。我们的结果确立了症候存储器能量代价的层级，并确定了控制子空间量子纠错理想热力学负担的码、噪声和测量结构。
英文摘要
Quantum error correction acts as an entropy pump, transferring noise-induced uncertainty from a protected quantum system into syndrome information stored in an auxiliary memory. Repeated operation requires this memory to be cleared which unavoidably contributes to the energetic cost of error correction. Here, we characterise this contribution for subspace quantum error-correcting codes and identify how it depends on the joint structure of the code, the noise, and the representation of the retained syndrome information. Starting from the Knill-Laflamme conditions, we construct an effective syndrome state whose von Neumann entropy sets a lower bound on the ideal work required to maintain a reusable syndrome register. Projective syndrome readout generally generates additional entropy, and we quantify the resulting gap through measurement inefficiency. We then specialise to stabiliser codes under independent local Pauli noise and analyse two classical levels of syndrome representation. At the level of abstract error labels, degeneracies among single-qubit errors reduce the leading-order entropy of processed recovery labels. At the parity-check level, lower-weight checks reduce the marginal entropy generated by individual measurement outcomes in the low-noise regime. We identify the additional burden associated with retaining and separately erasing these outcomes as a bit-level inefficiency, and illustrate both costs for the five-qubit, Steane, generalised Shor, and rotated surface codes. Our results establish a hierarchy of syndrome-memory energetic costs and identify the code, noise, and measurement structures that control the ideal thermodynamic burden of subspace quantum error correction.
Comments21 pages, 4 figures; Comments welcome!
