量子低密度格码
Quantum low-density lattice codes
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中文总结 AI 辅助
该研究基于经典低密度格码构造量子低密度格码，结合模拟消息传递译码器，其性能接近混合量子位-模拟译码器，将开源相关代码。
中文摘要 AI 辅助
戈特斯曼-基塔耶夫-普雷斯基尔（GKP）码提供了一类将离散量子信息（量子位）编码到无限维玻色模式中的有前景方案，这类方案基于数学格。当这类码与离散变量码级联时，已得到相对充分的研究，但原生GKP码的构造与译码仍基本处于未解决状态，原因是会遇到计算上困难的问题。为应对这一挑战，我们主张通过构造译码可行的格来协同设计译码器与量子纠错码本身：高效译码的要求有效决定了量子纠错码。该构造基于经典低密度格码（LDLC），即低密度奇偶校验码的格类似物，在此被提升为GKP码族。具体而言，我们引入了经典随机构造LDLC的量子版本。我们表明，经过适当降维后，这些码的码性能与同等模式数的级联GKP表面码相当或更优。不过，此处构造的GKP-LDLC不具有严格稀疏的奇偶校验矩阵，这促使我们研究原本为LDLC开发的原生模拟消息传递译码器应用于级联GKP-LDPC码时的性能。我们表明，全模拟线性时间译码器的性能接近最先进的混合量子位-模拟译码器。为促进未来关于一般GKP码的结构与性能的研究，相关源代码将通过开源Julia包在[链接1]和[链接2]发布。
英文摘要
Gottesman-Kitaev-Preskill (GKP) codes provide a family of promising schemes for encoding discrete quantum information (qudits) into infinite-dimensional bosonic modes based on mathematical lattices. While such codes, when concatenated with discrete-variable codes, are relatively well studied, the construction and decoding of native GKP codes has largely remained open due to the computationally hard problems encountered. To address this challenge, we advocate a strategy of co-designing the decoder and the quantum error-correcting code itself by constructing lattices for which decoding is feasible: The requirement of efficient decoding effectively determines the quantum error-correcting code. This construction is built on classical low-density lattice codes (LDLCs), a lattice analogue of low-density parity-check codes, here lifted to families of GKP codes. Concretely, we introduce quantum versions of classical, randomly constructed LDLCs. We show that after suitable dimensionality reduction these codes have code properties comparable to or better than concatenated GKP-surface codes of equal number of modes. However, the GKP-LDLCs constructed here do not have a strictly sparse parity check matrix, which motivates our study of the performance of natively analog message-passing decoders originally developed for LDLCs when applied to concatenated GKP-LDPC codes. We show that the fully analog, linear-time decoder achieves performances close to state-of-the-art hybrid qubit-analog decoders. To facilitate future research on the structure and performance of general GKP codes, the relevant source code will be released in open-source Julia packages LatticeDecoder.jl and SymplecticGKP.jl.
发表机构
- University of Sydney（悉尼大学）
- Chalmers University of Technology（查尔姆斯理工大学）
- Freie Universität Berlin（柏林自由大学）
- Helmholtz-Zentrum Berlin für Materialien und Energie（柏林亥姆霍兹材料能源中心）
- École Normale Supérieure, PSL University（巴黎高等师范学院，PSL大学）
机构由 AI 辅助整理，请以论文原文为准。
