Optimal number of parametrized rotations and Hadamard gates in parametrized Clifford circuits with non-repeated parameters
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913425440899072 |
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| author | Vandaele, Vivien Perdrix, Simon Vuillot, Christophe |
| author_facet | Vandaele, Vivien Perdrix, Simon Vuillot, Christophe |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07846 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal number of parametrized rotations and Hadamard gates in parametrized Clifford circuits with non-repeated parameters Vandaele, Vivien Perdrix, Simon Vuillot, Christophe Quantum Physics 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. |
| title | Optimal number of parametrized rotations and Hadamard gates in parametrized Clifford circuits with non-repeated parameters |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2407.07846 |