Quantum error correction with the toric Gottesman-Kitaev-Preskill code
Quantum error correction with the toric Gottesman-Kitaev-Preskill code
复制标题
DOI：
10.1103/physreva.99.032344
复制
发表时间：
2018-09
影响因子：
2.9
通讯作者：
Christophe Vuillot;H. Asasi;Yang Wang;L. Pryadko;B. Terhal
中科院分区：
文献类型：
--
作者：
Christophe Vuillot;H. Asasi;Yang Wang;L. Pryadko;B. Terhal
我们研究的性能的单模Gottesman-Kitaev-Preskill（GKP）代码和它的串联与复曲面代码的噪声模型的高斯位移，或位移误差。我们展示了如何可以优化的GKP码的重复噪声纠错中的错误跟踪。我们这样做，通过检查这个设置的最大似然问题，并将其映射到一个一维欧几里德路径积分建模粒子在随机余弦电位。我们证明了最小能量解码策略作为路径积分评估的代理的效率。在本文的第二部分，我们分析和数值评估的GKP码与复曲面码的级联。当复曲面码测量值和GKP纠错测量值都很理想时，我们发现通过使用GKP误差信息，复曲面码的阈值从10%提高到14%。当仅GKP误差校正测量是完美的时，我们观察到6%的阈值。在更现实的设置时，所有的错误信息是嘈杂的，我们展示了如何表示的最大似然解码问题的复曲面GKP代码作为一个3D紧凑的QED模型中存在的淬火随机规范场，随机plaquette规范模型的复曲面代码的扩展。我们提出了一个解码器，这个问题表明存在一个噪声阈值在移位误差标准偏差σ0 <$0.243复曲面码测量，数据错误和GKP辅助错误。如果误差仅来自不完美的GKP态，那么这对应于只有四个或更多光子的状态。我们的最后一个结果是一个不去的结果，线性振荡器代码，编码振荡器到振荡器。对于高斯位移误差模型，我们证明了编码对应于压缩位移误差。这表明线性振子码对于量子信息保护抵抗高斯移位错误是无用的。
We examine the performance of the single-mode Gottesman-Kitaev-Preskill (GKP) code and its concatenation with the toric code for a noise model of Gaussian shifts, or displacement errors. We show how one can optimize the tracking of errors in repeated noisy error correction for the GKP code. We do this by examining the maximum-likelihood problem for this setting and its mapping onto a 1D Euclidean path-integral modeling a particle in a random cosine potential. We demonstrate the efficiency of a minimum-energy decoding strategy as a proxy for the path integral evaluation. In the second part of this paper, we analyze and numerically assess the concatenation of the GKP code with the toric code. When toric code measurements and GKP error correction measurements are perfect, we find that by using GKP error information the toric code threshold improves from 10% to 14%. When only the GKP error correction measurements are perfect we observe a threshold at 6%. In the more realistic setting when all error information is noisy, we show how to represent the maximum likelihood decoding problem for the toric-GKP code as a 3D compact QED model in the presence of a quenched random gauge field, an extension of the random-plaquette gauge model for the toric code. We present a decoder for this problem which shows the existence of a noise threshold at shift-error standard deviation σ0 ≈ 0.243 for toric code measurements, data errors and GKP ancilla errors. If the errors only come from having imperfect GKP states, then this corresponds to states with just four photons or more. Our last result is a no-go result for linear oscillator codes, encoding oscillators into oscillators. For the Gaussian displacement error model, we prove that encoding corresponds to squeezing the shift errors. This shows that linear oscillator codes are useless for quantum information protection against Gaussian shift errors.