Quantum singular value transformation for an arbitrary bounded operator embedded in a unitary operator
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911759551430656 |
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| author | Kiumi, Chusei Suzuki, Akito |
| author_facet | Kiumi, Chusei Suzuki, Akito |
| contents | This research extends quantum singular value transformation (QSVT) for general bounded operators embedded in unitary operators on possibly infinite-dimensional Hilbert spaces. Through in-depth mathematical exploration, we have achieved a refined operator-theoretic understanding of QSVT, leading to a more streamlined approach. One of the key discoveries is that polynomial transformations in QSVT inherently apply to the entire operator, rather than being contingent on the selection of a specific basis. We expect that this research will pave the way for applying these insights to a broader range of problems in quantum information processing and provide analytical tools for quantum dynamics, such as quantum walks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09007 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum singular value transformation for an arbitrary bounded operator embedded in a unitary operator Kiumi, Chusei Suzuki, Akito Quantum Physics Mathematical Physics This research extends quantum singular value transformation (QSVT) for general bounded operators embedded in unitary operators on possibly infinite-dimensional Hilbert spaces. Through in-depth mathematical exploration, we have achieved a refined operator-theoretic understanding of QSVT, leading to a more streamlined approach. One of the key discoveries is that polynomial transformations in QSVT inherently apply to the entire operator, rather than being contingent on the selection of a specific basis. We expect that this research will pave the way for applying these insights to a broader range of problems in quantum information processing and provide analytical tools for quantum dynamics, such as quantum walks. |
| title | Quantum singular value transformation for an arbitrary bounded operator embedded in a unitary operator |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2401.09007 |