Complete characterization of the ground-space structure of two-body frustration-free Hamiltonians for qubits
- Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada)
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543 (Singapore)
- Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario N1G 2W1 (Canada)
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.
- OSTI ID:
- 22080377
- Journal Information:
- Physical Review. A, Vol. 84, Issue 4; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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