Optimal number of parametrized rotations and Hadamard gates in parametrized Clifford circuits with non-repeated parameters

• URL: http://arxiv.org/abs/2407.07846v1
• Date: Wed, 10 Jul 2024 17:08:18 GMT
• Title: Optimal number of parametrized rotations and Hadamard gates in parametrized Clifford circuits with non-repeated parameters
• Authors: Vivien Vandaele, Simon Perdrix, Christophe Vuillot,
• Abstract summary: We present an efficient algorithm to reduce the number of non-Clifford gates in quantum circuits. We show that this approach is optimal for parametrized circuits composed of Clifford gates and parametrized rotations.
• Score: 4.423586186569902
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present an efficient algorithm to reduce the number of non-Clifford gates in quantum circuits and the number of parametrized rotations in parametrized quantum circuits. The method consists in finding rotations that can be merged into a single rotation gate. This approach has already been considered before and is used as a pre-processing procedure in many optimization algorithms, notably for optimizing the number of Hadamard gates or the number of $T$ gates in Clifford$+T$ circuits. Our algorithm has a better complexity than similar methods and is particularly efficient for circuits with a low number of internal Hadamard gates. Furthermore, we show that this approach is optimal for parametrized circuits composed of Clifford gates and parametrized rotations with non-repeated parameters. For the same type of parametrized quantum circuits, we also prove that a previous procedure optimizing the number of Hadamard gates and internal Hadamard gates is optimal. This procedure is notably used in our low-complexity algorithm for optimally reducing the number of parametrized rotations.

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