Monte Carlo simulation of stoquastic Hamiltonians

Understand

Stoquastic Hamiltonians are characterized by the property that their off-diagonal matrix elements in the standard product basis are real and non-positive.

• Many interesting quantum models fall into this class including the Transverse field Ising Model (TIM), the Heisenberg model on bipartite graphs, and the bosonic Hubbard model.
• Here we consider the problem of estimating the ground state energy of a local stoquastic Hamiltonian $H$ with a promise that the ground state of $H$ has a non-negligible correlation with some `guiding' state that admits a concise classical description.
• A formalized version of this problem called Guided Stoquastic Hamiltonian is shown to be complete for the complexity class MA (a probabilistic analogue of NP).