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| Format: | Preprint |
| Veröffentlicht: |
2022
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| Online-Zugang: | https://arxiv.org/abs/2209.15025 |
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| _version_ | 1866911773968302080 |
|---|---|
| author | Lin, Ruge |
| author_facet | Lin, Ruge |
| contents | The concept of quantum representation of finite groups (QRFG) has been a fundamental aspect of quantum computing for quite some time, playing a role in every corner, from elementary quantum logic gates to the famous Shor's and Grover's algorithms. In this article, we provide a formal definition of this concept using both group theory and differential geometry. Our work proves the existence of a quantum representation for any finite group and outlines two methods for translating each generator of the group into a quantum circuit, utilizing gate decomposition of unitary matrices and variational quantum algorithms. Additionally, we provide numerical simulations of an explicit example on an open-access platform. Finally, we demonstrate the usefulness and potential of QRFG by showing its role in the implementation of some quantum algorithms and quantum finite automata. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_15025 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quantum representation of finite groups Lin, Ruge Quantum Physics The concept of quantum representation of finite groups (QRFG) has been a fundamental aspect of quantum computing for quite some time, playing a role in every corner, from elementary quantum logic gates to the famous Shor's and Grover's algorithms. In this article, we provide a formal definition of this concept using both group theory and differential geometry. Our work proves the existence of a quantum representation for any finite group and outlines two methods for translating each generator of the group into a quantum circuit, utilizing gate decomposition of unitary matrices and variational quantum algorithms. Additionally, we provide numerical simulations of an explicit example on an open-access platform. Finally, we demonstrate the usefulness and potential of QRFG by showing its role in the implementation of some quantum algorithms and quantum finite automata. |
| title | Quantum representation of finite groups |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2209.15025 |