Developing and expanding on the idea by Moore and Nilsson [1], we provide a detailed description of families of logspace uniform quantum circuits that implement cyclic shifts and permutations of qubits. This allows us to formally prove that such operations belong to QNC0, the quantum analogue of the complexity class NC0, which captures highly efficiently parallelizable classical computations.
Faro S., Pavone A., Viola C. (2024). Families of Constant-Depth Quantum Circuits for Rotations and Permutations. In U. de'Liguoro, M. Palazzo, L. Roversi (a cura di), Proceedings of the 25th Italian Conference on Theoretical Computer Science (pp. 29-41). CEUR-WS.
Families of Constant-Depth Quantum Circuits for Rotations and Permutations
Pavone A.;
2024-01-01
Abstract
Developing and expanding on the idea by Moore and Nilsson [1], we provide a detailed description of families of logspace uniform quantum circuits that implement cyclic shifts and permutations of qubits. This allows us to formally prove that such operations belong to QNC0, the quantum analogue of the complexity class NC0, which captures highly efficiently parallelizable classical computations.
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