Analog Information Decoding of Bosonic Quantum Low-Density Parity-Check Codes

Lucas Berent, Timo Hillmann, Jens Eisert, Robert Wille, Joschka Roffe
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Abstract

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 the 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.

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玻色子量子低密度奇偶校验码的模拟信息解码
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编码使用多个两级系统对逻辑信息进行编码,可能需要大量硬件。玻色码提供了另一种方法,它利用谐波振荡器的无穷维希尔伯特空间来编码量子信息。玻色子编码有两个很有前途的特点,一是综合征测量是本机模拟的,二是可以与离散变量编码串联。在这项工作中,我们提出了新颖的解码方法,这些方法明确利用了从玻色量子比特读出的串联架构中获得的模拟综合征信息。我们的方法用途广泛,可普遍应用于任何与量子低密度奇偶校验(QLDPC)码串联的玻色码。此外,我们还引入了准单发协议的概念,作为一种新方法,它能显著减少在现象学噪声下解码时所需的重复综合征测量次数。为实现该协议,我们首次针对一般 QLDPC 码采用重叠窗法实现了时域解码,并提出了一种新型模拟单次解码方法。我们的成果为使用模拟信息的通用解码算法奠定了基础,并在使用玻色子-QLDPC 码进行容错量子计算的方向上展示了前景广阔的成果。
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