The BoseHubbard model is QMAcomplete
Abstract
The BoseHubbard model is a system of interacting bosons that live on the vertices of a graph. The particles can move between adjacent vertices and experience a repulsive onsite interaction. The Hamiltonian is determined by a choice of graph that specifies the geometry in which the particles move and interact. We prove that approximating the ground energy of the BoseHubbard model on a graph at fixed particle number is QMAcomplete. In our QMAhardness proof, we encode the history of an nqubit computation in the subspace with at most one particle per site (i.e., hardcore bosons). This feature, along with the wellknown mapping between hardcore bosons and spin systems, lets us prove a related result for a class of 2local Hamiltonians defined by graphs that generalizes the XY model. By avoiding the use of perturbation theory in our analysis, we circumvent the need to multiply terms in the Hamiltonian by large coefficients.
 Publication:

arXiv eprints
 Pub Date:
 November 2013
 DOI:
 10.48550/arXiv.1311.3297
 arXiv:
 arXiv:1311.3297
 Bibcode:
 2013arXiv1311.3297C
 Keywords:

 Quantum Physics;
 Condensed Matter  Statistical Mechanics;
 Computer Science  Computational Complexity
 EPrint:
 Proceedings of the 41st International Colloquium on Automata, Languages, and Programming (ICALP 2014), pp. 308319 (2014)