论文标题
统一复合物共轭的最佳通用量子电路
Optimal universal quantum circuits for unitary complex conjugation
论文作者
论文摘要
令$ u_d $为一个统一运算符，代表任意$ d $维统一的量子操作。这项工作提出了最佳量子电路，用于将$ u_d $的数字$ k $转换为其复杂的共轭$ \ bar {u_d} $。我们的电路承认并行实现，并被证明对任何$ k $和$ d $都是最佳的，平均保真度为$ \ left \ langle {f} \ right \ rangle = \ frac {k+1} {d（d-k）} $。为平均忠诚度，噪声的鲁棒性和其他标准的功绩显示了最佳性。这扩展了以前的作品，这些作品考虑了操作$ u_d $的单个调用（$ k = 1 $）的场景，以及$ k = d-1 $呼叫的特殊情况。然后，我们表明我们的结果包括从$ u_d $的$ k $调用到$ f（u_d）$的最佳转换，从$ d $ d $ d $二维单位运算符的组中，由于复杂的共轭是唯一对整体运营商组的非平淡无奇的自动化。最后，我们将最佳的复杂共轭实现应用于设计概率电路，以逆转任意量子的演变。
Let $U_d$ be a unitary operator representing an arbitrary $d$-dimensional unitary quantum operation. This work presents optimal quantum circuits for transforming a number $k$ of calls of $U_d$ into its complex conjugate $\bar{U_d}$. Our circuits admit a parallel implementation and are proven to be optimal for any $k$ and $d$ with an average fidelity of $\left\langle{F}\right\rangle =\frac{k+1}{d(d-k)}$. Optimality is shown for average fidelity, robustness to noise, and other standard figures of merit. This extends previous works which considered the scenario of a single call ($k=1$) of the operation $U_d$, and the special case of $k=d-1$ calls. We then show that our results encompass optimal transformations from $k$ calls of $U_d$ to $f(U_d)$ for any arbitrary homomorphism $f$ from the group of $d$-dimensional unitary operators to itself, since complex conjugation is the only non-trivial automorphisms on the group of unitary operators. Finally, we apply our optimal complex conjugation implementation to design a probabilistic circuit for reversing arbitrary quantum evolutions.
