PIRSA:23100102

Universal, deterministic, and exact protocol to reverse qubit-unitary and qubit-encoding isometry operations

Yoshida, S. (2023). Universal, deterministic, and exact protocol to reverse qubit-unitary and qubit-encoding isometry operations. Perimeter Institute. https://pirsa.org/23100102

Yoshida, Satoshi. Universal, deterministic, and exact protocol to reverse qubit-unitary and qubit-encoding isometry operations. Perimeter Institute, Oct. 19, 2023, https://pirsa.org/23100102 

          @misc{ pirsa_PIRSA:23100102,
            doi = {10.48660/23100102},
            url = {https://pirsa.org/23100102},
            author = {Yoshida, Satoshi},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Universal, deterministic, and exact protocol to reverse qubit-unitary and qubit-encoding isometry operations},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {oct},
            note = {PIRSA:23100102 see, \url{https://pirsa.org}}
          }

Satoshi Yoshida

University of Tokyo

Talk number
PIRSA:23100102
Collection
Talk Type
Subject
Abstract

We report a deterministic and exact protocol to reverse any unknown qubit-unitary and qubit-encoding isometry operations. To avoid known no-go results on universal deterministic exact unitary inversion, we consider the most general class of protocols transforming unknown unitary operations within the quantum circuit model, where the input unitary operation is called multiple times in sequence and fixed quantum circuits are inserted between the calls. In the proposed protocol, the input qubit-unitary operation is called 4 times to achieve the inverse operation, and the output state in an auxiliary system can be reused as a catalyst state in another run of the unitary inversion. This protocol only applies only for qubit-unitary operations, but we extend this protocol to any qubit-encoding isometry operations. We also present the simplification of the semidefinite programming for searching the optimal deterministic unitary inversion protocol for an arbitrary dimension presented by M. T. Quintino and D. Ebler [Quantum 6, 679 (2022)]. We show a method to reduce the large search space representing all possible protocols, which provides a useful tool for analyzing higher-order quantum transformations for unitary operations.

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