发表机构
Iceberg Quantum（冰山量子）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出提升手术方法，利用QLDPC码的对称性实现快速并行逻辑测量，在保持低物理开销的同时将综合征测量轮数减少十倍，为低开销容错量子计算提供实用途径。
AI 中文摘要
量子低密度奇偶校验（QLDPC）码是实现低开销容错量子计算的主要候选方案。然而，QLDPC码中逻辑运算的时间开销仍然是一个关键挑战。码手术是一种用于容错逻辑测量的空间高效技术，其开销源于重复多轮的综合征测量。我们提出了提升手术，一种在阿贝尔群代数码上实现快速并行手术的方法，该方法保持了使QLDPC码具有吸引力的低物理开销。提升手术保留了底层码的对称性，使得搜索大规模实例变得可行，并为高效硬件实现提供了自然途径。我们利用块分解和交换代数技术来表征提升手术，研究性质良好的子族，并构造具体示例。特别地，我们提出了参数为$[[90, 8, 10]]$和$[[198, 8, 16]]$的量子径向码，其手术是快速、并行且可寻址的，允许在单轮综合征提取中测量任意一组同Pauli类型的独立逻辑算子。我们在电路级去极化噪声下对提升手术进行基准测试，对于$[[90, 8, 10]]$码，发现其逻辑性能与标准码手术相当，而所需的综合征测量轮数减少了十倍。通过结合速度和并行性，提升手术为低开销容错量子计算提供了一条实用途径。
英文摘要
Quantum low-density parity-check (QLDPC) codes are a leading candidate for achieving low-overhead fault-tolerant quantum computing. However, the time overhead of logical operations in QLDPC codes remains a key challenge. Code surgery, a space-efficient technique for fault-tolerant logical measurements, incurs this overhead through repeated rounds of syndrome measurement. We introduce lifted surgery, a method for fast and parallel surgery on Abelian group algebra codes that maintains the low physical overhead that makes QLDPC codes attractive. Lifted surgery preserves the symmetries of the underlying code, making searches for large instances tractable and offering a natural route towards efficient hardware implementations. We utilise block decompositions and techniques from commutative algebra to characterise lifted surgery, investigate well-behaved subfamilies, and construct explicit examples. In particular, we present quantum radial codes with parameters $[[90, 8, 10]]$ and $[[198, 8, 16 ]]$ for which surgery is fast, parallel, and addressable, allowing arbitrary sets of independent logical operators of the same Pauli type to be measured in a single round of syndrome extraction. We benchmark lifted surgery under circuit-level depolarising noise and, for the $[[ 90, 8, 10 ]]$ code, find logical performance comparable to standard code surgery while requiring ten times fewer rounds of syndrome measurement. By combining speed and parallelism, lifted surgery offers a practical route towards low-overhead fault-tolerant quantum computing.
Comments38 pages, 3 figures
