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Reversing Unknown Qubit-Unitary Operation, Deterministically and Exactly.
Satoshi Yoshida1, Akihito Soeda1,2,3, Mio Murao1,4
1Department of Physics, Graduate School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan.
Physical Review Letters
|October 6, 2023
Summary
Researchers developed a deterministic protocol to reverse unknown qubit-unitary operations, simulating time inversion. This quantum circuit method uses multiple calls to the operation and a reusable catalyst state for exact inversion.
Area of Science:
- Quantum Information Science
- Quantum Computing
- Quantum Control
Background:
- Reversing unknown quantum operations is crucial for quantum computation and simulation.
- Existing methods face limitations due to no-go theorems for universal deterministic exact unitary inversion.
Purpose of the Study:
- To propose a deterministic and exact protocol for reversing any unknown qubit-unitary operation.
- To simulate the time inversion of a closed qubit system.
- To overcome limitations of previous inversion protocols.
Main Methods:
- Utilizing the quantum circuit model with sequential calls to the unknown unitary operation.
- Inserting fixed quantum circuits between operation calls.
- Employing a protocol requiring 4 calls to the input qubit-unitary operation.
- Reusing an output state as a catalyst state for subsequent runs.
Main Results:
- A deterministic and exact protocol for inverting unknown qubit-unitary operations is presented.
- The protocol simulates time inversion in a closed qubit system.
- A simplified semidefinite programming method is introduced for optimizing deterministic unitary inversion protocols.
- A method to reduce the search space for quantum transformation protocols is demonstrated.
Conclusions:
- The proposed protocol offers an exact method for reversing unknown qubit-unitary operations.
- The developed techniques facilitate the analysis of higher-order quantum transformations.
- This work provides a valuable tool for advancing quantum information processing and control.
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