论文标题
量子代码不会增加针对各向同性错误的保真度
Quantum codes do not increase fidelity against isotropic errors
论文作者
论文摘要
给定$ m $ $ qubit $φ_0$和$（n，m） - $量子代码$ \ mathcal {c} $，让$φ$是$ n- $ qubit，是$ n-$ qubit，是$ \ nathcal {c} - $ $编码$φ_0$。假设状态$φ$受各向同性误差（折叠）的影响，变成$ψ$，并且$ \ MATHCAL {C} $的校正电路被应用于$ψ$，获得了量子状态$ \tildeφ$。另外，我们在不使用量子代码$ \ MATHCAL {C} $的情况下分析了各向同性错误的效果。在这种情况下，错误将$φ_0$转换为$ψ_0$。假设校正电路没有引入新的错误，并且不会增加执行时间，我们将比较$ψ$，$ \tildeφ$和$ψ_0$的保真度，以分析量子代码的幂来控制同位素错误。我们证明$ 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代码。
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.
