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The general problem of finding the ground state energy of lattice Hamiltonians is known to be very hard, even for a quantum computer.
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K. G. H. Vollbrecht, E. Solano, and J. I. Cirac, Phys. Rev. Lett. 93, 220502 (2004)
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Christina V. Kraus, Michael M. Wolf, and J. Ignacio Cirac, arXiv:quant-ph/0607094
Cited in the paper.
K. G. H. Vollbrecht, and J. I. Cirac, Phys. Rev. A 73, 012324 (2006)
2006
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D.J. Shepherd, T. Franz, R.F. Werner, Phys. Rev. Lett. 97 (2006) 020502; Diego de Falco, Dario Tamascelli, J. Phys. A: Math. Gen. 39 5873-5895 (2006)
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Later among the works it cites.
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