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The Quantum and Classical Complexity of Translationally Invariant Tiling and Hamiltonian Problems
[article]
2010
arXiv
pre-print
We study the complexity of a class of problems involving satisfying constraints which remain the same under translations in one or more spatial directions. In this paper, we show hardness of a classical tiling problem on an N x N 2-dimensional grid and a quantum problem involving finding the ground state energy of a 1-dimensional quantum system of N particles. In both cases, the only input is N, provided in binary. We show that the classical problem is NEXP-complete and the quantum problem is
arXiv:0905.2419v2
fatcat:vlgd4ofus5h43dzpgvjapn5fgy