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| complete characterization of the ground-space structure of two-body frustration-free hamiltonians for qubits | |
| Ji Zhengfeng; Wei Zhaohui; Zeng Bei | |
| 2011 | |
| Source | PHYSICAL REVIEW A
 |
| ISSN | 1050-2947 |
| Volume | 84Issue:4Pages:- |
| English Abstract | The problem of finding the ground state of a frustration-free Hamiltonian carrying only two-body interactions between qubits is known to be solvable in polynomial time. It is also shown recently that, for any such Hamiltonian, there is always a ground state that is a product of single- or two-qubit states. However, it remains unclear whether the whole ground space is of any succinct structure. Here, we give a complete characterization of the ground space of any two-body frustration-free Hamiltonian of qubits. Namely, it is a span of tree tensor network states of the same tree structure. This characterization allows us to show that the problem of determining the ground-state degeneracy is as hard as, but no harder than, its classical analog.; The problem of finding the ground state of a frustration-free Hamiltonian carrying only two-body interactions between qubits is known to be solvable in polynomial time. It is also shown recently that, for any such Hamiltonian, there is always a ground state that is a product of single- or two-qubit states. However, it remains unclear whether the whole ground space is of any succinct structure. Here, we give a complete characterization of the ground space of any two-body frustration-free Hamiltonian of qubits. Namely, it is a span of tree tensor network states of the same tree structure. This characterization allows us to show that the problem of determining the ground-state degeneracy is as hard as, but no harder than, its classical analog. |
| Indexed Type | SCI ; EI |
| Keyword | Characterization Ground State Plant Extracts Polynomial Approximation Trees (Mathematics) |
| Department | Ji Zhengfeng Perimeter Inst Theoret Phys Waterloo ON N2L 2Y5 Canada. Ji Zhengfeng Chinese Acad Sci State Key Lab Comp Sci Inst Software Beijing Peoples R China. Wei Zhaohui Natl Univ Singapore Ctr Quantum Technol Singapore 117543 Singapore. Zeng Bei Univ Guelph Dept Math & Stat Guelph ON N1G 2W1 Canada. Zeng Bei Univ Waterloo Inst Quantum Comp Waterloo ON N2L 3G1 Canada. |
| Subject | Optics ; Physics |
| Sponsorship | NSF of China60736011; Government of Canada through Industry Canada; Province of Ontario through the Ministry of Research Innovation; CQT WBSR-710-000-007-271, R-710-000-008-271; NSERC; CIFAR |
| Language | 英语 |
| WOS ID | WOS:000296284200002 |
| Citation statistics | |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/16073 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation GB/T 7714 | Ji Zhengfeng,Wei Zhaohui,Zeng Bei. complete characterization of the ground-space structure of two-body frustration-free hamiltonians for qubits[J]. PHYSICAL REVIEW A,2011,84(4):-. |
| APA | Ji Zhengfeng,Wei Zhaohui,&Zeng Bei.(2011).complete characterization of the ground-space structure of two-body frustration-free hamiltonians for qubits.PHYSICAL REVIEW A,84(4),-. |
| MLA | Ji Zhengfeng,et al."complete characterization of the ground-space structure of two-body frustration-free hamiltonians for qubits".PHYSICAL REVIEW A 84.4(2011):-. |
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