AI 中文总结
介绍自适应模拟退火算法，用于寻找高编码率和大距离的中等规模量子纠错码，目标是CSS码和SWEL码，通过能量函数引导搜索，找到的码达到或超量子吉尔伯特 - 瓦尔沙莫夫界变体，可用于容错架构和高速码演示。
AI 中文摘要
我们引入一种自适应模拟退火算法，以寻找具有高编码率和大距离的中等规模量子纠错码。搜索目标为两类稳定器码：（1）CSS码；（2）我们称为“具有等效逻辑的自对偶”（SWEL）码的CSS码子类，后者允许逻辑哈达玛门和相位门的横向实现。搜索由一个能量函数引导，该函数替代码容量噪声模型中的逻辑错误率，结合码距和最小重量逻辑算子计数解决阻碍朴素距离优化的离散平台。对于多达50个物理量子比特的块长度，搜索找到的CSS和SWEL码达到或超过量子吉尔伯特 - 瓦尔沙莫夫界变体。这些码不仅为基于码级联的容错架构提供良好种子码，也是近期量子计算硬件高速码演示的有前景候选者。
英文摘要
We introduce an adaptive simulated annealing algorithm to search for moderately-sized quantum error-correcting codes with high encoding rates and large distances. Our search targets two classes of stabilizer codes: (1) CSS codes, and (2) a subclass of CSS codes that we call ``self-dual with equivalent logicals'' (SWEL) codes, the latter of which which admit transversal implementations of logical Hadamard and phase gates that can be leveraged to construct fault-tolerant gate sets. The search is guided by an energy function that acts as a surrogate for the logical error rate in a code-capacity noise model, combining code distance with a count of minimum-weight logical operators to resolve the discrete plateaux that impede naïve distance optimization. For block lengths of up to $50$ physical qubits, our search finds state-of-the-art CSS and SWEL codes whose distances frequently meet or exceed the variants of the quantum Gilbert-Varshamov bound. In addition to providing favorable seed codes for fault-tolerant architectures based on code concatenation, the codes found in this work are promising candidates for high-rate code demonstrations on near-term quantum computing hardware.
