arXiv 2201.085892022-01-21quant-ph

量子码不增加对各向同性错误的保真度

Quantum codes do not increase fidelity against isotropic errors

J. Lacalle, L. M. Pozo-Coronado, A. L. Fonseca de Oliveira, R. Martin-Cuevas

摘要：

给定$m-$量子位$Φ_0$和$(n,m)-$量子码$\mathcal{C}$，令$Φ$是由$Φ_0$的$\mathcal{C}-$编码产生的$n-$量子位。假设状态$Φ$受到各向同性误差（退相干）的影响，变为$Ψ$，并且将$\mathcal{C}$的校正电路应用于$Ψ$，获得量子状态$\tildeΦ$。或者，我们分析各向同性错误的影响，而不使用量子码$\mathcal{C}$。在这种情况下，错误将$Φ_0$转换为$Ψ_0$。假设校正电路不引入新的错误并且不增加执行时间，我们比较了$Ψ$、$\tildeΦ$和$Ψ_0$的保真度，目的是分析量子码控制各向同性错误的能力。我们证明了$F(Ψ_0) \geq F(\tildeΦ) \geq F(Ψ)$ .因此，针对各向同性错误优化保真度的最佳选择是不使用量子码。

英文摘要：

Given an $m-$qubit $Φ_0$ and an $(n,m)-$quantum code $\mathcal{C}$, let $Φ$ be the $n-$qubit that results from the $\mathcal{C}-$encoding of $Φ_0$. Suppose that the state $Φ$ is affected by an isotropic error (decoherence), becoming $Ψ$, and that the corrector circuit of $\mathcal{C}$ is applied to $Ψ$, obtaining the quantum state $\tildeΦ$. Alternatively, we analyze the effect of the isotropic error without using the quantum code $\mathcal{C}$. In this case the error transforms $Φ_0$ into $Ψ_0$. Assuming that the correction circuit does not introduce new errors and that it does not increase the execution time, we compare the fidelity of $Ψ$, $\tildeΦ$ and $Ψ_0$ with the aim of analyzing the power of quantum codes to control isotropic errors. We prove that $F(Ψ_0) \geq F(\tildeΦ) \geq F(Ψ)$. Therefore the best option to optimize fidelity against isotropic errors is not to use quantum codes.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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