Reversing Unknown Qubit-Unitary Operation, Deterministically and Exactly

Abstract

We report a deterministic and exact protocol to reverse any unknown qubit-unitary operation, which simulates the time inversion of a closed qubit system. 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. 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 $\text{6}$, 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.

6+20 pages, 2+4 figures. All codes are available at https://github.com/sy3104/deterministic_exact_unitary_inversion

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• Semidefinite programming relaxations for quantum correlations
• Experimental Aspects of Indefinite Causal Order in Quantum Mechanics
• Energy-Consumption Advantage of Quantum Computation
• Experimental superposition of time directions
• Experimental demonstration of input-output indefiniteness in a single quantum device
• Reversing Unknown Quantum Processes via Virtual Combs for Channels with Limited Information
• Higher-order quantum transformations of Hamiltonian dynamics
• Linear programming with unitary-equivariant constraints
• Interplay between the Hilbert-space dimension of a control system and the memory induced by a quantum SWITCH
• Parallel-in-time quantum simulation via Page and Wootters quantum time
• Achieving the Multi-parameter Quantum Cramér-Rao Bound with Antiunitary Symmetry
• Universal adjointation of isometry operations using conversion of quantum supermaps
• Parameterized quantum comb and simpler circuits for reversing unknown qubit-unitary operations
• Characterising transformations between quantum objects, 'completeness' of quantum properties, and transformations without a fixed causal order
• Analytical Lower Bound on Query Complexity for Transformations of Unknown Unitary Operations
• Iterative construction of ${\mathfrak{S}}_p\times {\mathfrak{S}}_p$ group-adapted irreducible matrix units for the walled Brauer algebra