Optimal number of parametrized rotations and Hadamard gates in parametrized Clifford circuits with non-repeated parameters
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 gates in Clifford 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.
Keywords
Cite
@article{arxiv.2407.07846,
title = {Optimal number of parametrized rotations and Hadamard gates in parametrized Clifford circuits with non-repeated parameters},
author = {Vivien Vandaele and Simon Perdrix and Christophe Vuillot},
journal= {arXiv preprint arXiv:2407.07846},
year = {2024}
}