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arXiv · 2407.07846

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

Vivien Vandaele·Simon Perdrix·Christophe Vuillot
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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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Vivien Vandaele, Simon Perdrix, Christophe Vuillot. 2024-07-10. Optimal number of parametrized rotations and Hadamard gates in parametrized Clifford circuits with non-repeated parameters. https://arxiv.org/abs/2407.07846

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