TY - JOUR
T1 - The Bose-Hubbard model is QMA-complete
JF - Proceedings of the 41st International Colloquium on Automata, Languages, and Programming (ICALP 2014)
Y1 - 2014
A1 - Andrew M. Childs
A1 - David Gosset
A1 - Zak Webb
AB - The Bose-Hubbard 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 on-site 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 Bose-Hubbard model on a graph at fixed particle number is QMA-complete. In our QMA-hardness proof, we encode the history of an n-qubit computation in the subspace with at most one particle per site (i.e., hard-core bosons). This feature, along with the well-known mapping between hard-core bosons and spin systems, lets us prove a related result for a class of 2-local 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.
VL - 8572
U4 - 308-319
UR - http://arxiv.org/abs/1311.3297v1
J1 - Proceedings of the 41st International Colloquium on Automata
U5 - 10.1007/978-3-662-43948-7_26
ER -