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Subject: Optics ; Physics
Title:
complete characterization of the ground-space structure of two-body frustration-free hamiltonians for qubits
Author: Ji Zhengfeng ; Wei Zhaohui ; Zeng Bei
Keyword: Characterization ; Ground state ; Plant extracts ; Polynomial approximation ; Trees (mathematics)
Source: PHYSICAL REVIEW A
Issued Date: 2011
Volume: 84, Issue:4, Pages:-
Indexed Type: SCI ; EI
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.
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
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.
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.
Language: 英语
WOS ID: WOS:000296284200002
Citation statistics:
Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/16073
Appears in Collections:软件所图书馆_期刊论文

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Recommended Citation:
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,2011-01-01,84(4):-.
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