Goto Hayato
RIKEN Center for Quantum Computing (RQC), Wako, Saitama 351-0198, Japan.
Corporate Research & Development Center, Toshiba Corporation, 1 Komukai Toshiba-cho, Saiwai-ku, Kawasaki-shi 212-8582, Japan.
Sci Adv. 2024 Sep 6;10(36):eadp6388. doi: 10.1126/sciadv.adp6388. Epub 2024 Sep 4.
Standard approaches to quantum error correction for fault-tolerant quantum computing are based on encoding a single logical qubit into many physical ones, resulting in asymptotically zero encoding rates and therefore huge resource overheads. To overcome this issue, high-rate quantum codes, such as quantum low-density parity-check codes, have been studied over the past decade. In this case, however, it is difficult to perform logical gates in parallel while maintaining low overheads. Here, we propose concatenated high-rate small-size quantum error-detecting codes as a family of high-rate quantum codes. Their simple structure allows for a geometrical interpretation using hypercubes corresponding to logical qubits. We thus call them many-hypercube codes. They can realize both high rates, e.g., 30% (64 logical qubits are encoded into 216 physical ones), and parallelizability of logical gates. Developing dedicated decoder and encoders, we achieve high error thresholds even in a circuit-level noise model. Thus, the many-hypercube codes will pave the way to high-performance fault-tolerant quantum computing.
用于容错量子计算的标准量子纠错方法是基于将单个逻辑量子比特编码到多个物理量子比特中，这导致渐近零编码率，从而产生巨大的资源开销。为了克服这个问题，在过去十年中人们研究了高速量子码，比如量子低密度奇偶校验码。然而，在这种情况下，要在保持低开销的同时并行执行逻辑门是很困难的。在这里，我们提出级联高速小尺寸量子错误检测码作为一类高速量子码。它们简单的结构允许使用与逻辑量子比特相对应的超立方体进行几何解释。因此我们称它们为多超立方体码。它们既能实现高速率，例如30%（64个逻辑量子比特被编码到216个物理量子比特中），又能实现逻辑门的并行性。通过开发专用的解码器和编码器，即使在电路级噪声模型中，我们也能实现高错误阈值。因此，多超立方体码将为高性能容错量子计算铺平道路。
