Holomorphic representation of quantum computations
We study bosonic quantum computations using the Segal-Bargmann representation of quantum states. We argue that this holomorphic representation is a natural one which not only gives a canonical description of bosonic quantum computing using basic elements of complex analysis but also provides a unify...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2022-10-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2022-10-06-831/pdf/ |
| _version_ | 1811196417724645376 |
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| author | Ulysse Chabaud Saeed Mehraban |
| author_facet | Ulysse Chabaud Saeed Mehraban |
| author_sort | Ulysse Chabaud |
| collection | DOAJ |
| description | We study bosonic quantum computations using the Segal-Bargmann representation of quantum states. We argue that this holomorphic representation is a natural one which not only gives a canonical description of bosonic quantum computing using basic elements of complex analysis but also provides a unifying picture which delineates the boundary between discrete- and continuous-variable quantum information theory. Using this representation, we show that the evolution of a single bosonic mode under a Gaussian Hamiltonian can be described as an integrable dynamical system of classical Calogero-Moser particles corresponding to the zeros of the holomorphic function, together with a conformal evolution of Gaussian parameters. We explain that the Calogero-Moser dynamics is due to unique features of bosonic Hilbert spaces such as squeezing. We then generalize the properties of this holomorphic representation to the multimode case, deriving a non-Gaussian hierarchy of quantum states and relating entanglement to factorization properties of holomorphic functions. Finally, we apply this formalism to discrete- and continuous- variable quantum measurements and obtain a classification of subuniversal models that are generalizations of Boson Sampling and Gaussian quantum computing. |
| first_indexed | 2024-04-12T00:58:21Z |
| format | Article |
| id | doaj.art-d7465f9d26654bf497b9a03d0b21a09c |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-04-12T00:58:21Z |
| publishDate | 2022-10-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-d7465f9d26654bf497b9a03d0b21a09c2022-12-22T03:54:34ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2022-10-01683110.22331/q-2022-10-06-83110.22331/q-2022-10-06-831Holomorphic representation of quantum computationsUlysse ChabaudSaeed MehrabanWe study bosonic quantum computations using the Segal-Bargmann representation of quantum states. We argue that this holomorphic representation is a natural one which not only gives a canonical description of bosonic quantum computing using basic elements of complex analysis but also provides a unifying picture which delineates the boundary between discrete- and continuous-variable quantum information theory. Using this representation, we show that the evolution of a single bosonic mode under a Gaussian Hamiltonian can be described as an integrable dynamical system of classical Calogero-Moser particles corresponding to the zeros of the holomorphic function, together with a conformal evolution of Gaussian parameters. We explain that the Calogero-Moser dynamics is due to unique features of bosonic Hilbert spaces such as squeezing. We then generalize the properties of this holomorphic representation to the multimode case, deriving a non-Gaussian hierarchy of quantum states and relating entanglement to factorization properties of holomorphic functions. Finally, we apply this formalism to discrete- and continuous- variable quantum measurements and obtain a classification of subuniversal models that are generalizations of Boson Sampling and Gaussian quantum computing.https://quantum-journal.org/papers/q-2022-10-06-831/pdf/ |
| spellingShingle | Ulysse Chabaud Saeed Mehraban Holomorphic representation of quantum computations Quantum |
| title | Holomorphic representation of quantum computations |
| title_full | Holomorphic representation of quantum computations |
| title_fullStr | Holomorphic representation of quantum computations |
| title_full_unstemmed | Holomorphic representation of quantum computations |
| title_short | Holomorphic representation of quantum computations |
| title_sort | holomorphic representation of quantum computations |
| url | https://quantum-journal.org/papers/q-2022-10-06-831/pdf/ |
| work_keys_str_mv | AT ulyssechabaud holomorphicrepresentationofquantumcomputations AT saeedmehraban holomorphicrepresentationofquantumcomputations |