Further Applications of the Generalised Phase Kick-Back
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916447000723456 |
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| author | Ossorio-Castillo, Joaquín Pastor-Díaz, Ulises Tornero, José M. |
| author_facet | Ossorio-Castillo, Joaquín Pastor-Díaz, Ulises Tornero, José M. |
| contents | In our previous work, we defined a quantum algorithmic technique known as the Generalised Phase Kick-Back, or $GPK$, and analysed its applications in generalising some classical quantum problems, such as the Deutsch-Jozsa problem or the Bernstein-Vazirani problem. We also proved that using this technique we can solve Simon's problem in a more efficient manner. In this paper we continue analysing the potential of this technique, defining the concept of $\mathbf{y}$-balanced functions and solving a new problem, which further generalises the generalised Deutsch-Jozsa problem (the fully balanced image problem). This problem also underlines the relation between quantum computation and Boolean function theory, and, in particular, the Walsh and Fourier-Hadamard transforms. We finish our discussion by solving the generalised version of Simon's problem using the $GPK$ algorithm, while analysing the efficiency of this new solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03850 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Further Applications of the Generalised Phase Kick-Back Ossorio-Castillo, Joaquín Pastor-Díaz, Ulises Tornero, José M. Quantum Physics 68Q12, 68Q09, 81P68 In our previous work, we defined a quantum algorithmic technique known as the Generalised Phase Kick-Back, or $GPK$, and analysed its applications in generalising some classical quantum problems, such as the Deutsch-Jozsa problem or the Bernstein-Vazirani problem. We also proved that using this technique we can solve Simon's problem in a more efficient manner. In this paper we continue analysing the potential of this technique, defining the concept of $\mathbf{y}$-balanced functions and solving a new problem, which further generalises the generalised Deutsch-Jozsa problem (the fully balanced image problem). This problem also underlines the relation between quantum computation and Boolean function theory, and, in particular, the Walsh and Fourier-Hadamard transforms. We finish our discussion by solving the generalised version of Simon's problem using the $GPK$ algorithm, while analysing the efficiency of this new solution. |
| title | Further Applications of the Generalised Phase Kick-Back |
| topic | Quantum Physics 68Q12, 68Q09, 81P68 |
| url | https://arxiv.org/abs/2405.03850 |