Floquet 阿贝尔多循环码
Floquet Abelian Multicycle Codes
AI总结：
该研究提出Floquet AMC码，构造AMC4实例得到特定参数的Floquet存储器，在EM3噪声模型下测得伪阈值约1.2%，实现了高维同调冗余的紧凑仅测量量子码。
AI中文摘要：
阿贝尔多循环（AMC）码是紧凑的量子低密度奇偶校验码，其多块链复形结构提供冗余的低重量稳定子并支持单次错误校正。我们通过在有限阿贝尔群代数上推导一般j阶、D维AMC复形的商格表示，将该格提升至时空，并在相关ZX网络中旋转电路时间方向，引入了Floquet AMC码。当校验和数据蜘蛛具有偶价且允许面向时间的局部端口匹配时，该网络分解为原生两量子比特XX和ZZ测量的周期调度。我们构造了广义自行车和2阶AMC4实例，确定了它们的瞬时稳定子群，并通过最小化所有不等价电路切割计算其嵌入距离。对于局部等价于四维环面码的AMC4实例，我们获得了参数为[[108,6,5]]、[[144,6,8]]和[[324,6,10]]的Floquet存储器。在测量原生EM3噪声模型下的局部Pauli网检测器模板和波束搜索解码，得到约1.2%的伪阈值估计。这些结果提供了高维同调冗余的紧凑仅测量实现，无需直接测量原始重量六稳定子。
英文摘要：
Abelian multicycle (AMC) codes are compact quantum low-density parity-check codes whose multiblock chain-complex structure provides redundant low-weight stabilizers and supports single-shot error correction. We introduce Floquet AMC codes by deriving a quotient-lattice representation of a general level-$j$, $D$-dimensional AMC complex over a finite Abelian group algebra, lifting this lattice to spacetime, and rotating the circuit-time direction in the associated ZX network. When the check and data spiders have even valence and admit a time-oriented local port matching, the network decomposes into a periodic schedule of native two-qubit $XX$ and $ZZ$ measurements. We construct generalized-bicycle and level-$2$ AMC4 examples, determine their instantaneous stabilizer groups, and compute their embedded distances by minimizing over all inequivalent circuit cuts. For AMC4 instances locally equivalent to four-dimensional toric codes, we obtain Floquet memories with parameters $[[108,6,5]]$, $[[144,6,8]]$, and $[[324,6,10]]$. Local Pauli-web detector templates and beam-search decoding under the measurement-native EM3 noise model yield an estimated pseudothreshold of approximately $1.2\%$. These results provide compact measurement-only realizations of higher-dimensional homological redundancy without directly measuring the original weight-six stabilizers.
