Quantum error correction is crucial for scalable quantum information processing applications. Traditional discrete-variable quantum codes that use multiple two-level systems to encode logical information can be hardware-intensive. An alternative approach is provided by bosonic codes, which use the infinite-dimensional Hilbert space of harmonic oscillators to encode quantum information. Two promising features of bosonic codes are that syndrome measurements are natively analog and that they can be concatenated with discrete-variable codes. In this work, we propose novel decoding methods that explicitly exploit the analog syndrome information obtained from the bosonic qubit readout in a concatenated architecture. Our methods are versatile and can be generally applied to any bosonic code concatenated with a quantum low-density parity-check (QLDPC) code. Furthermore, we introduce the concept of quasi-single-shot protocols as a novel approach that significantly reduces the number of repeated syndrome measurements required when decoding under phenomenological noise. To realize the protocol, we present a first implementation of time-domain decoding with the overlapping window method for general QLDPC codes, and a novel analog single-shot decoding method. Our results lay the foundation for general decoding algorithms using analog information and demonstrate promising results in the direction of fault-tolerant quantum computation with concatenated bosonic-QLDPC codes.

翻译：量子纠错对于可扩展量子信息处理应用至关重要。传统上采用多级二能级系统编码逻辑信息的离散变量量子码可能带来硬件密集型问题。玻色码提供了一种替代方案，它利用谐振子的无限维希尔伯特空间编码量子信息。玻色码的两个显著特征是：纠错测量天然具有模拟特性，且可与离散变量码级联。本文提出新型译码方法，明确利用级联架构中从玻色量子比特读取获得的模拟纠错信息。该方法具有通用性，可普遍适用于与量子低密度奇偶校验码级联的任何玻色码。此外，我们引入准单次译码协议概念，该创新方法能显著减少在现象学噪声下译码所需的重复纠错测量次数。为实现该协议，我们首次提出基于重叠窗口方法的时间域译码实现方案，适用于通用量子LDPC码，并设计出新型模拟单次译码方法。本文研究成果为利用模拟信息的通用译码算法奠定基础，并展示了级联玻色-量子LDPC码在容错量子计算方向的广阔前景。