Qudit-Basis Universal Quantum Computation Using X[superscript (2)]
We prove that universal quantum computation can be realized—using only linear optics and χ[superscript (2)] (three-wave mixing) interactions—in any (n+1)-dimensional qudit basis of the n-pump-photon subspace. First, we exhibit a strictly universal gate set for the qubit basis in the one-pump-photon...
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| 格式: | 文件 |
| 语言: | English |
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American Physical Society
2018
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| 在线阅读: | http://hdl.handle.net/1721.1/114792 https://orcid.org/0000-0002-0013-416X https://orcid.org/0000-0001-7296-523X https://orcid.org/0000-0002-6094-5861 |
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| author | Niu, Yuezhen Chuang, Isaac Shapiro, Jeffrey H |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Niu, Yuezhen Chuang, Isaac Shapiro, Jeffrey H |
| author_sort | Niu, Yuezhen |
| collection | MIT |
| description | We prove that universal quantum computation can be realized—using only linear optics and χ[superscript (2)] (three-wave mixing) interactions—in any (n+1)-dimensional qudit basis of the n-pump-photon subspace. First, we exhibit a strictly universal gate set for the qubit basis in the one-pump-photon subspace. Next, we demonstrate qutrit-basis universality by proving that χ[superscript (2)] Hamiltonians and photon-number operators generate the full u(3) Lie algebra in the two-pump-photon subspace, and showing how the qutrit controlled-Z gate can be implemented with only linear optics and χ[superscript (2)] interactions. We then use proof by induction to obtain our general qudit result. Our induction proof relies on coherent photon injection or subtraction, a technique enabled by χ[superscript (2)] interaction between the encoding modes and ancillary modes. Finally, we show that coherent photon injection is more than a conceptual tool, in that it offers a route to preparing high-photon-number Fock states from single-photon Fock states. |
| first_indexed | 2024-09-23T08:58:47Z |
| format | Article |
| id | mit-1721.1/114792 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:58:47Z |
| publishDate | 2018 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1147922022-09-30T12:35:22Z Qudit-Basis Universal Quantum Computation Using X[superscript (2)] Niu, Yuezhen Chuang, Isaac Shapiro, Jeffrey H Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Department of Physics Massachusetts Institute of Technology. Research Laboratory of Electronics Niu, Yuezhen Chuang, Isaac Shapiro, Jeffrey H We prove that universal quantum computation can be realized—using only linear optics and χ[superscript (2)] (three-wave mixing) interactions—in any (n+1)-dimensional qudit basis of the n-pump-photon subspace. First, we exhibit a strictly universal gate set for the qubit basis in the one-pump-photon subspace. Next, we demonstrate qutrit-basis universality by proving that χ[superscript (2)] Hamiltonians and photon-number operators generate the full u(3) Lie algebra in the two-pump-photon subspace, and showing how the qutrit controlled-Z gate can be implemented with only linear optics and χ[superscript (2)] interactions. We then use proof by induction to obtain our general qudit result. Our induction proof relies on coherent photon injection or subtraction, a technique enabled by χ[superscript (2)] interaction between the encoding modes and ancillary modes. Finally, we show that coherent photon injection is more than a conceptual tool, in that it offers a route to preparing high-photon-number Fock states from single-photon Fock states. United States. Air Force Office of Scientific Research (Grant FA9550-14-1-0052) 2018-04-19T15:19:11Z 2018-04-19T15:19:11Z 2018-04 2017-11 2018-04-18T18:00:14Z Article http://purl.org/eprint/type/JournalArticle 0031-9007 1079-7114 http://hdl.handle.net/1721.1/114792 Niu, Murphy Yuezhen et al. "Qudit-Basis Universal Quantum Computation Using X[superscript (2)]." Physical Review Letters 120, 16 (April 2018): 160502 © 2018 American Physical Society https://orcid.org/0000-0002-0013-416X https://orcid.org/0000-0001-7296-523X https://orcid.org/0000-0002-6094-5861 en http://dx.doi.org/10.1103/PhysRevLett.120.160502 Physical Review Letters Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Niu, Yuezhen Chuang, Isaac Shapiro, Jeffrey H Qudit-Basis Universal Quantum Computation Using X[superscript (2)] |
| title | Qudit-Basis Universal Quantum Computation Using X[superscript (2)] |
| title_full | Qudit-Basis Universal Quantum Computation Using X[superscript (2)] |
| title_fullStr | Qudit-Basis Universal Quantum Computation Using X[superscript (2)] |
| title_full_unstemmed | Qudit-Basis Universal Quantum Computation Using X[superscript (2)] |
| title_short | Qudit-Basis Universal Quantum Computation Using X[superscript (2)] |
| title_sort | qudit basis universal quantum computation using x superscript 2 |
| url | http://hdl.handle.net/1721.1/114792 https://orcid.org/0000-0002-0013-416X https://orcid.org/0000-0001-7296-523X https://orcid.org/0000-0002-6094-5861 |
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