Finite Rate QLDPC-GKP Coding Scheme that Surpasses the CSS Hamming Bound
Finite Rate QLDPC-GKP Coding Scheme that Surpasses the CSS Hamming Bound
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DOI：
10.22331/q-2022-07-20-767
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发表时间：
2021-11
期刊：
影响因子：
6.4
通讯作者：
N. Raveendran;Narayanan Rengaswamy;F. Rozpędek;Ankur Raina;Liang Jiang;Bane Vasi'c
中科院分区：
文献类型：
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作者：
N. Raveendran;Narayanan Rengaswamy;F. Rozpędek;Ankur Raina;Liang Jiang;Bane Vasi'c
量子纠错最近被证明可从编码量子比特的特定物理编码中极大获益。特别是，一些研究人员考虑了用连续变量戈特斯曼 - 基塔耶夫 - 普雷斯克尔（GKP）码对单个编码量子比特进行编码，然后在这些GKP量子比特上施加一种外层离散变量码，比如表面码。在这样一种级联方案下，来自内层GKP纠错的模拟信息提高了外层码的噪声阈值。然而，表面码的码率趋近于零，并且随着距离增加需要大量资源。在这项工作中，我们将GKP码与通用量子低密度奇偶校验（QLDPC）码进行级联，并展示了一种在迭代解码算法中利用GKP模拟信息的自然方法。我们首先给出了两个提升积QLDPC码族的噪声阈值，然后展示了当迭代解码器（一种对硬件友好的最小和算法（MSA））利用GKP模拟信息时噪声阈值的提高情况。我们还表明，当GKP模拟信息与MSA的顺序更新时间表相结合时，该方案超过了这些码族中著名的CSS汉明界。此外，我们观察到GKP模拟信息有助于迭代解码器避开QLDPC码的坦纳图中的有害陷阱集，从而消除或显著降低逻辑错误率曲线的错误平底。最后，我们讨论了这项工作中出现的关于GKP模拟信息下的信道容量以及改进解码器设计和分析的新的基础和实际问题。
Quantum error correction has recently been shown to benefit greatly from specific physical encodings of the code qubits. In particular, several researchers have considered the individual code qubits being encoded with the continuous variable GottesmanKitaev-Preskill (GKP) code, and then imposed an outer discrete-variable code such as the surface code on these GKP qubits. Under such a concatenation scheme, the analog information from the inner GKP error correction improves the noise threshold of the outer code. However, the surface code has vanishing rate and demands a lot of resources with growing distance. In this work, we concatenate the GKP code with generic quantum low-density parity-check (QLDPC) codes and demonstrate a natural way to exploit the GKP analog information in iterative decoding algorithms. We first show the noise thresholds for two lifted product QLDPC code families, and then show the improvements of noise thresholds when the iterative decoder – a hardware-friendly min-sum algorithm (MSA) – utilizes the GKP analog information. We also show that, when the GKP analog information is combined with a sequential update schedule for MSA, the scheme surpasses the well-known CSS Hamming bound for these code families. Furthermore, we observe that the GKP analog information helps the iterative decoder in escaping harmful trapping sets in the Tanner graph of the QLDPC code, thereby eliminating or significantly lowering the error floor of the logical error rate curves. Finally, we discuss new fundamental and practical questions that arise from this work on channel capacity under GKP analog information, and on improving decoder design and analysis.