CQuIC Seminars
The Bose-Hubbard model is QMA-complete
Presented by David Gosset, IQC
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 entirely by a choice of graph that determines 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. Our QMA-hardness proof encodes 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, allows us to prove a related result for a class of 2-local Hamiltonians defined by graphs that generalizes the XY model. This is joint work with Andrew Childs.
3:30 pm, Thursday, December 5, 2013
PAIS-2540, PAIS
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