Probabilistic storage and retrieval (PSR) of unitary quantum dynamics is possible with exponentially small failure probability with respect to the number of systems used as a quantum memory [M. Sedlák, A. Bisio, and M. Ziman, Phys. Rev. Lett. 122, 170502 (2019)]. Here we study improvements due to a priori knowledge about the unitary transformation to be stored. In particular, we study $N\to 1$ PSR of qubit phase gates, i.e., qubit rotations around the $Z$ axis with an unknown angle, and show that if we access the gate only $N$ times the optimal probability of perfect retrieving of its single use is $N/(N+1)$. We propose a quantum circuit realization for the optimal protocol and show that a programmable phase gate [G. Vidal, L. Masanes, and J. I. Cirac, Phys. Rev. Lett. 88, 047905 (2002)] can be turned into a $(2^k-1)\to 1$ optimal PSR of phase gates and requires only $k$ controlled-not gates, while having exponentially small failure probability in $k$.

中文翻译：

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量子位相门的概率存储和检索

相对于用作量子存储器的系统数量，单一量子动力学的概率存储和检索（PSR）可能具有极小的故障概率。Sedlák，A。Bisio和M. Ziman，物理学。牧师 122，170502（2019）]。在这里，我们研究由于要存储的关于transformation变换的先验知识而产生的改进。特别地，我们研究$ñ\to \mathrm{1个}$ 量子位相位门的PSR，即围绕位的量子位旋转 $ž$ 轴的角度未知，并表明如果我们仅访问门 $ñ$ 完美回收其一次使用的最佳概率乘以 $ñ/（ñ+\mathrm{1个}）$。我们提出了一种用于最佳协议的量子电路实现，并显示了可编程的相位门[G. Vidal，L。Masanes和J. I. Cirac，物理学。牧师 88，047905（2002）]可以变成一个$（2^{ķ}-\mathrm{1个}）\to \mathrm{1个}$ 相位门的最佳PSR，仅需 $ķ$受控而不是门，而在$ķ$。