Probabilistic storage and retrieval of qubit phase gates

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 $N\to 1$ 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 $(2^k-1)\to 1$ optimal PSR of phase gates and requires only $k$ CNOT gates, while having exponentially small failure probability in $k$.

arXiv comment9 pages, 7 figures

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Cited by in corpus (7)

• Symmetries of quantum evolutions
• Universal construction of decoders from encoding black boxes
• Storage and retrieval of von Neumann measurements
• Universal adjointation of isometry operations using conversion of quantum supermaps
• Robustness of optimal probabilistic storage and retrieval of unitary channels to noise
• Quantum Advantage in Storage and Retrieval of Isometry Channels
• Analytical Lower Bound on Query Complexity for Transformations of Unknown Unitary Operations