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的量子信息处理应用至关重要。传统的离散变量量子码使用多个二能级系统编码逻辑信息，可能导致硬件开销较大。玻色编码提供了另一种途径，它利用谐振子的无限维希尔伯特空间编码量子信息。玻色编码具有两个显著优势：其校验子测量本质上是模拟的，且能与离散变量码进行级联。本研究提出了新颖的解码方法，在级联架构中显式利用从玻色量子比特读出获取的模拟校验子信息。我们的方法具有通用性，可应用于任何与量子低密度奇偶校验码级联的玻色码。此外，我们引入了准单次协议的概念作为创新方法，在现象学噪声下的解码过程中显著减少了所需重复校验子测量的次数。为实现该协议，我们首次实现了通用QLDPC码基于重叠窗口法的时域解码，并提出了一种新型模拟单次解码方法。我们的研究成果为使用模拟信息的通用解码算法奠定了基础，并在级联玻色-QLDPC码的容错量子计算方向上展现出良好前景。