发表机构
Simula UiB; Department of Informatics, University of Bergen（Simula UiB; 卑尔根大学信息系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出局部自同构感知综合征编译（LocalASC），通过边轨道变量约简求解CSS量子LDPC码的深度最优综合征提取调度，并给出双块码与量子Tanner码的构造条件。
AI 中文摘要
Calderbank-Shor-Steane（CSS）量子低密度奇偶校验码的低深度综合征提取可被表述为一个受量子奇偶约束限制的适当有序边着色问题。CSS Tanner图的适当边着色确保每个数据或辅助量子比特在每一层中至多参与一个双量子比特门，但并不能保证X和Z校验测量的有效交错，因为对于每一对重叠的X/Z校验，X相互作用先于Z相互作用的共享数据量子比特数必须为偶数。在满足量子奇偶约束的适当有序边着色中，颜色的最小数量等于当每个稳定子校验使用单个辅助量子比特测量时的最小双量子比特深度。我们引入了局部自同构感知综合征编译（LocalASC），该方法将约束系统约简为Tanner图自同构子群下的边轨道变量，并将每个可行的轨道分配提升到整个图。尽管对于已发表的重量为6的IBM双变量自行车码，6层度下界无法达到，但我们表明这并非双块CSS码中的普遍现象。在最大校验重量等于最大Tanner图度的码实例中，LocalASC为几个具有奇数分量重量的双块CSS码（包括具有不相等奇数重量的实例）找到了深度最优的综合征提取调度。我们还为满足相同度条件的几个量子Tanner码获得了达到下界的综合征提取调度。为了在不计算Tanner图完整自同构群的情况下获得LocalASC所使用的子群，我们为阿贝尔群上的双块群代数CSS码构造了平移子群。对于量子Tanner码，我们给出了方形复形对称性扩展到Tanner图自同构的条件。
英文摘要
Low-depth syndrome extraction for Calderbank-Shor-Steane (CSS) quantum low-density parity-check codes can be formulated as a proper ordered edge-coloring problem subject to quantum parity constraints. A proper edge-coloring of the CSS Tanner graph ensures that each data or ancilla qubit participates in at most one two-qubit gate per layer, but does not guarantee a valid interleaving of the X- and Z-check measurements as for every overlapping X/Z check pair, the number of shared data qubits on which the X interaction precedes the Z interaction must be even. The minimum number of colors in a proper ordered edge-coloring satisfying the quantum parity constraints equals the minimum two-qubit depth when each stabilizer check is measured with a single ancilla. We introduce local automorphism-aware syndrome compilation (LocalASC), which reduces the constraint system to edge-orbit variables under a subgroup of the Tanner graph automorphisms and lifts each feasible orbit assignment to the full graph. Although the $6$-layer degree lower bound is unattainable for the published weight-$6$ IBM bivariate bicycle codes, we show that this is not universal among two-block CSS codes. Among code instances for which the maximum check weight equals the maximum Tanner graph degree, LocalASC finds depth-optimal syndrome-extraction schedules for several two-block CSS codes with odd component weights, including instances with unequal odd weights. We also obtain lower-bound-saturating syndrome-extraction schedules for several quantum Tanner codes satisfying the same degree condition. To obtain the subgroups used by LocalASC without computing the full automorphism group of the Tanner graph, we construct translation subgroups for two-block group-algebra CSS codes over abelian groups. For quantum Tanner codes, we give conditions under which square-complex symmetries extend to Tanner graph automorphisms.
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