Ground-state spaces of frustration-free Hamiltonians

Journal of Mathematical Physics

Volumn 53, Issue 10, 2012, Pages

  Chen, Jianxin ^a,b   Ji, Zhengfeng ^b,c   Kribs, David ^a,b   Wei, Zhaohui ^d   Zeng, Bei ^a,b  

^a UNIVERSITY OF GUELPH   (Canada)

^b UNIVERSITY OF WATERLOO   (Canada)

^c INSTITUTE OF SOFTWARE   (China)

^d NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84868353552     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4748527     Document Type: Article

References (18)

1. Bravyi S. Efficient algorithm for a quantum analogue of 2-SAT. e-print arXiv:quant-ph/0602108.
2. Bravyi S. Terhal B. Complexity of stoquastic frustration-free Hamiltonians. SIAM J. Comput. 2009, 39(4):1462-1485. 10.1137/08072689X, and
3. Chen J. Chen X. Duan R. Ji Z. Zeng B. No-go theorem for one-way quantum computing on naturally occurring two-level systems. Phys. Rev. A 2011, 83(5):050301(R). 10.1103/PhysRevA.83.050301, and
4. Chen J. Ji Z. Ruskai M.B. Zeng B. Zhou D.-L. Comment on some results of Erdahl and the convex structure of reduced density matrices. J. Math. Phys. 2012, 53(7):072203. 10.1063/1.4736842, and
5. Cohn P.M. Basic Algebra: Groups, Rings, and Fileds 2002, (Springer),.
6. Davey B.A. Priestley H.A. Introduction to Lattices and Order 2002, and (Cambridge University Press, Cambridge, England),.
7. Fritz T. Abstract convexity. Seminar on Mathematical Optimization 2009, in Magdeburg.
8. Fritz T. Convex spaces I: Definition and examples. e-print arXiv:0903.5522.
9. Hasan M.Z. Kane C.L. Colloquium: Topological insulators. Rev. Mod. Phys. 2010, 82:3045-3067. 10.1103/RevModPhys.82.3045, and
10. Ji Z. Wei Z. Zeng B. Complete characterization of the ground space structure of two-body frustration-free Hamiltonians for qubits. Phys. Rev. A 2011, 84(4):042338. 10.1103/PhysRevA.84.042338, and
11. Kalmbach G. Orthomodular Lattices (London Mathematical Society Monographs) 1983, (Academic, Cambridge, England),.
12. Kempe J. Kitaev A. Regev O. The complexity of the local hamiltonian problem. SIAM J. Comput. 2006, 35(5):1070. 10.1137/S0097539704445226, and
13. Kitaev A. Laumann C. Topological phases and quantum computation. and e-print arXiv:0904.2771.
14. Kitaev A. Shen A.H. Vyalyi M.N. Classical and Quantum Computation (Graduate Studies in Mathematics) 2002, and (American Mathematical Society),.
15. Liu Y.-K. Consistency of local density matrices is QMA-complete. Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques 2006, 438-449. (Springer),, pp.
16. Perez-Garcia D. Verstraete F. Cirac J.I. Wolf M.M. PEPS as unique ground states of local Hamiltonians. Quantum Inf. Comput. 2008, 8(6):650-663. and
17. Rockafellar R.T. Convex Analysis 1996, (Princeton University Press),.
18. Tsui D.C. Stormer H.L. Gossard A.C. Two-dimensional magnetotransport in the extreme quantum limit. Phys. Rev. Lett. 1982, 48(22):1559. 10.1103/PhysRevLett.48.1559, and