Performance and structure of single-mode bosonic codes
Performance and structure of single-mode bosonic codes
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DOI：
10.1103/physreva.97.032346
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发表时间：
2018-03-30
影响因子：
2.9
通讯作者：
Jiang, Liang
中科院分区：
文献类型：
--
作者：
Albert, Victor V.;Noh, Kyungjoo;Jiang, Liang
早期的 Gottesman、Kitaev 和 Preskill (GKP) 在振荡器中编码量子位的提议最近被猫和二项式代码提议所遵循。还提出了数值优化代码，我们在这里介绍这种类型的代码。这些代码尚未使用相同的错误模型进行比较；我们通过确定最佳恢复操作后所有代码相对于玻色纯损耗通道（即光子损耗）的纠缠保真度来提供这样的比较。然后，我们通过计算每个代码的通道散列界限来比较组合编码错误恢复通道可实现的通信速率。 Cat 和二项式代码的性能类似，其中二项式代码在丢失率较小的情况下优于 Cat 代码。尽管 GKP 代码的设计目的不是为了防止纯丢失信道，但对于大多数丢失率值而言，GKP 代码的性能都显着优于所有其他代码。我们表明，GKP 和一些二项式代码的性能随着代码平均光子数的增加而单调增加。为了证实我们在小丢失率下发生的猫二项式 GKP 性能顺序的数值证据，我们分析评估了这些代码的量子纠错条件。对于 GKP 码，我们在消失损失率的极限下发现了纠缠保真度的本质奇点。除了比较代码之外，我们还对二项式代码和离散变量系统进行了比较。首先，我们根据自旋相干态来表征一模和双模二项式以及多量子位排列不变码。这种特征使我们能够为二项式代码引入检查运算符和纠错过程。其次，我们引入了自旋相干态的推广，将我们的表征扩展到 qudit 二项式代码并产生了 multiqudit 代码。
The early Gottesman, Kitaev, and Preskill (GKP) proposal for encoding a qubit in an oscillator has recently been followed by cat-and binomial-code proposals. Numerically optimized codes have also been proposed, and we introduce codes of this type here. These codes have yet to be compared using the same error model; we provide such a comparison by determining the entanglement fidelity of all codes with respect to the bosonic pure-loss channel (i.e., photon loss) after the optimal recovery operation. We then compare achievable communication rates of the combined encoding-error-recovery channel by calculating the channel's hashing bound for each code. Cat and binomial codes perform similarly, with binomial codes outperforming cat codes at small loss rates. Despite not being designed to protect against the pure-loss channel, GKP codes significantly outperform all other codes for most values of the loss rate. We show that the performance of GKP and some binomial codes increases monotonically with increasing average photon number of the codes. In order to corroborate our numerical evidence of the cat-binomial-GKP order of performance occurring at small loss rates, we analytically evaluate the quantum error-correction conditions of those codes. For GKP codes, we find an essential singularity in the entanglement fidelity in the limit of vanishing loss rate. In addition to comparing the codes, we draw parallels between binomial codes and discrete-variable systems. First, we characterize one-and two-mode binomial as well as multiqubit permutation-invariant codes in terms of spin-coherent states. Such a characterization allows us to introduce check operators and error-correction procedures for binomial codes. Second, we introduce a generalization of spin-coherent states, extending our characterization to qudit binomial codes and yielding a multiqudit code.