发表机构
Institute for Quantum Computing Analytics (PGI-12), Forschungszentrum Jülich; Theoretical Physics, Universität des Saarlandes; Forschungszentrum Jülich（于利希研究中心量子计算分析研究所; 萨尔兰州立大学理论物理; 于利希研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对GKP码提出概率性误差消除方法，比较Steane型和隐形传态纠错，计算方形与六边形码的采样开销，并分析有限压缩噪声的影响，展示了连续变量码中纠错与缓解的非平凡结合。
AI 中文摘要
为了在量子计算机上解决实际问题，有必要使用容错量子纠错方案来克服噪声：即由物理元件不完美性引起的误差。Gottesman-Kitaev-Preskill（GKP）码旨在通过在一个或多个连续变量模式的希尔伯特空间中编码有限维逻辑子空间，以硬件高效的方式实现这一目标。然而，在近期实现中，完全消除误差是不可行的，因此自然地需要将替代性误差缓解技术与纠错结合使用。在本工作中，我们研究了在GKP码背景下一种称为概率性误差消除的量子误差缓解方法。我们比较了Steane型和基于隐形传态的GKP纠错，并计算了该方法在方形和六边形GKP码中的采样开销。我们利用GKP码的稳定子子系统分解，为噪声操作获得一个有效的逻辑信道，该信道用于表达目标逻辑酉的理想信道。我们考虑了数据和纠错所需的两个辅助模式上的有限压缩噪声，并检查了不同解码方法下采样开销与噪声之间的关系。我们的结果是针对单比特和两比特GKP Clifford门以及一轮纠错计算的，并展示了连续变量码中纠错与缓解的非平凡组合。
英文摘要
In order to solve practical problems on a quantum computer, it is necessary to use fault-tolerant quantum error correction schemes to overcome noise: the errors arising from imperfections in physical components. The Gottesman-Kitaev-Preskill (GKP) code aims at achieving this in a hardware efficient manner by encoding finite-dimensional logical subspaces in the Hilbert space of one or more continuous variable modes. In near term implementations, however, it is not feasible to eliminate errors entirely, so it is natural to also employ alternative error mitigation techniques together with error correction. In this work, we study a quantum error mitigation method known as probabilistic error cancellation in the context of the GKP code. We compare Steane-type and teleportation-based GKP error correction, and calculate the sampling overheads associated with the technique for square and hexagonal GKP codes. We employ the stabilizer subsystem decomposition for GKP codes to obtain an effective logical channel for noisy operations that is used to express the ideal one of a target logical unitary. We consider noise from finite squeezing on the data and the two ancilla modes, needed for error correction, and examine the relationship between the sampling overhead and the noise for different decoding methods. Our results are calculated for single- and two-qubit GKP Clifford gates and one round of error correction, and show the nontrivial combination of error correction and mitigation in continuous variable codes.
