Probabilistic storage and retrieval of qubit phase gates

TL;DR

This paper investigates probabilistic storage and retrieval of qubit phase gates, demonstrating optimal success probabilities and efficient quantum circuit implementations that leverage prior knowledge about the gates.

Contribution

It introduces an optimal protocol for $N ightarrow 1$ PSR of qubit phase gates and shows how to efficiently realize it with minimal quantum resources.

Findings

Optimal success probability for $N$-access storage of phase gates is $N/(N+1)$.

Proposed quantum circuit achieves the optimal protocol with minimal CNOT gates.

Programmable phase gates can be transformed into optimal PSR protocols with exponentially small failure.

Abstract

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 [PRL 122, 170502 (2019)]. Here we study improvements due to a priori knowledge about the unitary transformation to be stored. In particular, we study $N \rightarrow 1$ PSR of qubit phase gates, i.e. qubit rotations a round $Z$ 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 programmable phase gate [PRL 88, 047905 (2002)] can be turned into $(2^k-1)\rightarrow 1$ optimal PSR of phase gates and requires only $k$ CNOT gates, while having exponentially small failure probability in $k$.