发表机构
RIKEN Center for Quantum Computing; Toshiba Corporation（理化学研究所量子计算中心; 东芝公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究将多超立方体（MHC）码扩展至素数维度量子位元，构造了二、三级MHC码并推广逐级最小距离译码器，发现其错误阈值随维度提升，q=13时达10.0%，性能优于量子比特，为高维FTQC架构提供支撑。
AI 中文摘要
量子位元（qudits）比量子比特（qubits）拥有更大的局域希尔伯特空间，近来作为高效容错量子计算（FTQC）的构建模块受到关注。本研究将高速级联量子码——多超立方体（MHC）码，从量子比特扩展到素数维度q的量子位元。我们分别构造了参数为[[6²,4²,2²]]_q的二级MHC码和参数为[[6³,4³,2³]]_q的三级MHC码，并推广了最初为量子比特MHC码提出的逐级最小距离（LLMD）译码器。在量子位元X错误模型中，我们评估了维度q≤13时量子位元MHC码的码容量性能，发现错误阈值随局域维度q单调递增，q=13时达到10.0%，几乎是量子比特5.1%值的两倍。此外，在足够大的局域维度下，我们观察到显著的瀑布区，其中逻辑错误率的下降速度远快于传统基于距离的估计值。为理解观测到的量子位元优势的起源，我们基于底层q元噪声信道的熵分析译码性能，该分析揭示了更大q下可用校正子信息的增加，与固定熵下典型物理错误权重的同时增长之间存在竞争。这些结果表明，高维量子系统可显著提升高速级联量子码的性能，并推动基于量子位元的FTQC架构的进一步发展。
英文摘要
Qudits provide a larger local Hilbert space than qubits and have recently attracted interest as building blocks for efficient fault-tolerant quantum computation (FTQC). In this work, we extend many-hypercube (MHC) codes, high-rate concatenated quantum codes, from qubits to qudits of prime dimension $q$. We construct the level-2 and level-3 MHC codes with parameters $\left[\!\left[6^2,4^2,2^2\right]\!\right]_q$ and $\left[\!\left[6^3,4^3,2^3\right]\!\right]_q$, respectively, and generalize the level-by-level minimum-distance (LLMD) decoder originally proposed for the qubit MHC codes. In a qudit $X$-error model, we evaluate the code-capacity performance of the qudit MHC codes for dimensions up to $q=13$. We find that the error threshold increases monotonically with the local dimension $q$, reaching $10.0\%$ for $q=13$, nearly double the value of $5.1\%$ for qubits. Furthermore, for sufficiently large local dimensions, we observe a pronounced waterfall regime in which the logical error rate decreases substantially faster than expected from conventional distance-based estimates. To understand the origin of the observed qudit advantage, we analyze the decoding performance in terms of the entropy of the underlying $q$-ary noise channel. This analysis reveals a competition between the increased syndrome information available at larger $q$ and the simultaneous growth of the typical physical error weight at fixed entropy. These results demonstrate that higher-dimensional quantum systems can substantially improve the performance of high-rate concatenated quantum codes and motivate further development of qudit-based FTQC architectures.
Comments11 pages, 2 figures
