CQuIC Seminars
Monte carlo simulation of stoquastic hamiltonians
Presented by Sergey Bravyi, IBM
Hamiltonians avoiding the sign problem aka stoquastic are
characterized by the property that their off-diagonal matrix elements
in the standard basis are real and non-positive. Many interesting
quantum models fall into this class including Hamiltonians describing
quantum annealing algorithms, the transverse field Ising model (TIM),
the Heisenberg model on bipartite graphs, and the bosonic Hubbard model.
I will consider the problem of estimating the ground state energy of a
local stoquastic Hamiltonian and describe two special cases of this
problem amenable to classical randomized algorithms:
(1) Ferromagnetic TIM and
(2) Guided Stoquastic Hamiltonian.
The second problem includes an extra promise that the ground state has a
non-negligible overlap with a sufficiently simple "guiding" state
whose amplitudes can be efficiently computed. I will show that Ferromagnetic TIM can be
solved in polynomial time on a classical probabilistic computer whereas
Guided Stoquastic Hamiltonian is contained in the complexity class MA
(probabilistic analogue of NP).
3:30 pm, Thursday, February 13, 2014
PAIS-2540, PAIS
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