发表机构
Pritzker School of Molecular Engineering, The University of Chicago; Chicago Quantum Institute（芝加哥大学普里茨克分子工程学院; 芝加哥量子研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种直接从稳定子群定义的固有度量，用于量化综合征提取所需的相互作用，并据此推导出任意稳定子码的硬件相关深度下界，同时构建反例并建立渐近紧致的空间-深度权衡。
AI 中文摘要
在具有给定连通图的硬件上提取稳定子码的综合征，从根本上需要多少时间？先前Delfosse--Beverland--Tremblay（2021）和Baspin--Fawzi--Shayeghi（2023）的工作建立了将综合征提取与量子硬件上的局域性约束联系起来的界限。在这里，我们通过首先直接从稳定子群中制定一个用于综合征提取所需的相互作用的固有度量来解决这个问题，该度量独立于用于描述码的生成集。然后我们证明，该度量对任意稳定子码产生了精确综合征提取深度的依赖于硬件的下界。在该度量的指导下，我们还构建了具有常数深度局域综合征提取的环形曲面码示例，为DBT21的推论1提供了反例。此外，对于固定的量子Tanner族，该度量加强了BFS23中明确陈述的深度界限，并与我们的匹配构造一起，建立了渐近紧致的空间-深度权衡。在理论上，我们的结果将综合征提取所需的信息与设备的通信容量联系起来；而在实践中，它们提供了一种在承诺硬件布局之前评估不可避免的电路成本的方法。
英文摘要
How much time is fundamentally required to extract the syndrome of a stabilizer code on hardware with a given connectivity graph? Previous bounds answer through a chosen list of checks (Delfosse, Beverland, and Tremblay, 2021) or through the global code parameters (Baspin, Fawzi, and Shayeghi, 2023). Here, we show that neither determines the interaction that a particular hardware cut requires. We therefore define the intrinsic cut cost, $χ$, directly from the stabilizer group, independent of the generating set used to describe the code. It is computable from the check matrix alone, and equals the mutual information across the cut in the maximally mixed code state. We show that every exact extraction circuit, however adaptive, needs at least $χ/2$ two-qubit operations across the cut, and alternatively with free local processing exactly $χ$ shared Bell pairs. Guided by this intrinsic cut cost, we construct annular surface codes with constant-depth local extraction that give a counterexample to Corollary 1 of Delfosse, Beverland, and Tremblay. Furthermore, for a fixed quantum Tanner family, $χ$ grows at least linearly with the size of every sufficiently small region, giving a depth guarantee at each corresponding bottleneck in every layout. This strengthens the global perspective of Baspin, Fawzi, and Shayeghi and, together with our matching square-grid construction, yields a tight space--depth tradeoff. Our results connect the interaction required by syndrome extraction to hardware communication capacity and thus provide a way to assess unavoidable circuit costs before committing to a particular layout.
Comments70 pages, 2 figures, 5 tables. Revised exposition and references; expanded worked examples
