On the Walsh and Fourier-Hadamard Supports of Boolean Functions From a Quantum Viewpoint
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910436395319296 |
|---|---|
| author | Carlet, Claude Pastor-Díaz, Ulises Tornero, José María |
| author_facet | Carlet, Claude Pastor-Díaz, Ulises Tornero, José María |
| contents | In this paper, we focus on the links between Boolean function theory and quantum computing. In particular, we study the notion of what we call fully-balanced functions and analyse the Fourier--Hadamard and Walsh supports of those functions having such property. We study the Walsh and Fourier supports of other relevant classes of functions, using what we call balancing sets. This leads us to revisit and complete certain classic results and to propose new ones.
We complete our study by extending the previous results to pseudo-Boolean functions (in relation to vectorial functions) and giving an insight on its applications in the analysis of the possibilities that a certain family of quantum algorithms can offer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_09222 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the Walsh and Fourier-Hadamard Supports of Boolean Functions From a Quantum Viewpoint Carlet, Claude Pastor-Díaz, Ulises Tornero, José María Combinatorics Logic 15A99, 68R05, 94D10 F.4.1 In this paper, we focus on the links between Boolean function theory and quantum computing. In particular, we study the notion of what we call fully-balanced functions and analyse the Fourier--Hadamard and Walsh supports of those functions having such property. We study the Walsh and Fourier supports of other relevant classes of functions, using what we call balancing sets. This leads us to revisit and complete certain classic results and to propose new ones. We complete our study by extending the previous results to pseudo-Boolean functions (in relation to vectorial functions) and giving an insight on its applications in the analysis of the possibilities that a certain family of quantum algorithms can offer. |
| title | On the Walsh and Fourier-Hadamard Supports of Boolean Functions From a Quantum Viewpoint |
| topic | Combinatorics Logic 15A99, 68R05, 94D10 F.4.1 |
| url | https://arxiv.org/abs/2205.09222 |