Gottesman-Kitaev-Preskill纠错与退相干资源
Gottesman-Kitaev-Preskill error-correction with decohered resources
- Center for Theoretical Physics, Polish Academy of Sciences（波兰科学院理论物理中心）
- Faculty of Physics, University of Warsaw（华沙大学物理学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究分析纯退相位噪声下GKP纠错协议，发现隐形传态将纠错转化为累积的泡利-高斯噪声，导致码不再自纠错并产生泄漏，且泄漏随轮次饱和，影响运动振荡器平台。
AI中文摘要：
基于隐形传态的Gottesman-Kitaev-Preskill（GKP）纠错通常假设一个无退相干的GKP辅助贝尔对，这一理想化难以与玻色子系统中普遍存在的环境退相干相协调。在此，我们分析了GKP协议在纯退相位过程（在现实情境中普遍存在）下的性能。我们证明，在这类相互作用下，隐形传态不再将输入投影到GKP子空间，而是将GKP纠错转化为一种相关的泡利-高斯噪声过程，该过程可在连续的纠错轮次中累积。因此，与先前研究的含噪GKP场景不同，该码不再自我纠正。此外，重复的含噪GKP隐形传态会将编码模式驱离逻辑子空间，逐渐降低编码码字的保真度。我们表明，由此产生的泄漏随纠错轮次的数量迅速饱和。最后，我们研究了我们的结果对基于运动振荡器的GKP纠错平台的影响。
英文摘要：
Teleportation-based Gottesman-Kitaev-Preskill (GKP) error correction typically assumes a decoherence-free GKP ancilla Bell pair, an idealization that is difficult to reconcile with the ubiquitous environmental decoherence in bosonic systems. Here, we analyze the performance of the GKP protocol subject to pure-dephasing processes, ubiquitous in realistic situations. We show that, under this class of interactions, teleportation, instead of projecting the input onto the GKP subspace, transforms GKP error correction into a correlated Pauli-Gaussian noise process that can accumulate over successive correction rounds. Thus, unlike in previously studied noisy GKP scenarios, the code no longer self-corrects. Moreover, repeated noisy GKP teleportation drives the encoded modes out of the logical subspace, progressively degrading the encoded codewords. We show that the resulting leakage rapidly saturates with the number of correction rounds. Finally, we investigate the implications of our results for motional-oscillator-based GKP error-correction platforms.
