I will describe an efficient algorithm for finding the ground state of an n-particle quantum system subject to a 1D local Hamiltonian with a spectral gap. This amounts to solving for the lowest eigenvector of a succinctly described linear operator on an exponential dimensional space -- the kind of challenge that certain counting problems also encounter. This is joint work with I. Arad, U. Vazirani, and T. Vidick.

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