No-go theorem for one-way quantum computing on naturally occurring two-level systems
The ground states of some many-body quantum systems can serve as resource states for the one-way quantum computing model, achieving the full power of quantum computation. Such resource states are found, for example, in spin-5/2 and spin-3/2 systems. It is, of course, desirable to have a natural reso...
| Main Authors: | , , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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American Physical Society
2011
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| Online Access: | http://hdl.handle.net/1721.1/65640 |
| _version_ | 1826212882733334528 |
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| author | Chen, Jianxin Chen, Xie Duan, Runyao Ji, Zhengfeng Zeng, Bei |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Chen, Jianxin Chen, Xie Duan, Runyao Ji, Zhengfeng Zeng, Bei |
| author_sort | Chen, Jianxin |
| collection | MIT |
| description | The ground states of some many-body quantum systems can serve as resource states for the one-way quantum computing model, achieving the full power of quantum computation. Such resource states are found, for example, in spin-5/2 and spin-3/2 systems. It is, of course, desirable to have a natural resource state in a spin-1/2, that is, qubit system. Here, we give a negative answer to this question for frustration-free systems with two-body interactions. In fact, it is shown to be impossible for any genuinely entangled qubit state to be a nondegenerate ground state of any two-body frustration-free Hamiltonian. What is more, we also prove that every spin-1/2 frustration-free Hamiltonian with two-body interaction always has a ground state that is a product of single- or two-qubit states. In other words, there cannot be any interesting entanglement features in the ground state of such a qubit Hamiltonian. |
| first_indexed | 2024-09-23T15:39:39Z |
| format | Article |
| id | mit-1721.1/65640 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:39:39Z |
| publishDate | 2011 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/656402022-09-29T15:18:14Z No-go theorem for one-way quantum computing on naturally occurring two-level systems Chen, Jianxin Chen, Xie Duan, Runyao Ji, Zhengfeng Zeng, Bei Massachusetts Institute of Technology. Department of Physics Chen, Xie Chen, Xie The ground states of some many-body quantum systems can serve as resource states for the one-way quantum computing model, achieving the full power of quantum computation. Such resource states are found, for example, in spin-5/2 and spin-3/2 systems. It is, of course, desirable to have a natural resource state in a spin-1/2, that is, qubit system. Here, we give a negative answer to this question for frustration-free systems with two-body interactions. In fact, it is shown to be impossible for any genuinely entangled qubit state to be a nondegenerate ground state of any two-body frustration-free Hamiltonian. What is more, we also prove that every spin-1/2 frustration-free Hamiltonian with two-body interaction always has a ground state that is a product of single- or two-qubit states. In other words, there cannot be any interesting entanglement features in the ground state of such a qubit Hamiltonian. Natural Sciences and Engineering Research Council of Canada (NSERC) National Natural Science Foundation of China University of Technology, Sydney 2011-09-09T20:28:13Z 2011-09-09T20:28:13Z 2011-05 2010-08 Article http://purl.org/eprint/type/JournalArticle 0031-9007 http://hdl.handle.net/1721.1/65640 Chen, Jianxin et al. “No-go theorem for one-way quantum computing on naturally occurring two-level systems.” Physical Review A 83 (2011). ©2011 American Physical Society. en_US http://dx.doi.org/10.1103/PhysRevA.83.050301 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. application/pdf American Physical Society APS |
| spellingShingle | Chen, Jianxin Chen, Xie Duan, Runyao Ji, Zhengfeng Zeng, Bei No-go theorem for one-way quantum computing on naturally occurring two-level systems |
| title | No-go theorem for one-way quantum computing on naturally occurring two-level systems |
| title_full | No-go theorem for one-way quantum computing on naturally occurring two-level systems |
| title_fullStr | No-go theorem for one-way quantum computing on naturally occurring two-level systems |
| title_full_unstemmed | No-go theorem for one-way quantum computing on naturally occurring two-level systems |
| title_short | No-go theorem for one-way quantum computing on naturally occurring two-level systems |
| title_sort | no go theorem for one way quantum computing on naturally occurring two level systems |
| url | http://hdl.handle.net/1721.1/65640 |
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