Determining QMC simulability with geometric phases
- URL: http://arxiv.org/abs/2012.02022v1
- Date: Thu, 3 Dec 2020 16:07:07 GMT
- Title: Determining QMC simulability with geometric phases
- Authors: Itay Hen
- Abstract summary: We provide a construction for non-stoquastic, yet sign-problem-free and hence QMC-simulable, quantum many-body models.
We also demonstrate why the simulation of truly sign-problematic models using the QMC weights of the stoquasticized Hamiltonian is generally sub-optimal.
- Score: 0.4061135251278187
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Although stoquastic Hamiltonians are known to be simulable via
sign-problem-free quantum Monte Carlo (QMC) techniques, the non-stoquasticity
of a Hamiltonian does not necessarily imply the existence of a QMC sign
problem. We give a sufficient and necessary condition for the QMC-simulability
of Hamiltonians in a fixed basis in terms of geometric phases associated with
the chordless cycles of the weighted graphs whose adjacency matrices are the
Hamiltonians. We use our findings to provide a construction for non-stoquastic,
yet sign-problem-free and hence QMC-simulable, quantum many-body models. We
also demonstrate why the simulation of truly sign-problematic models using the
QMC weights of the stoquasticized Hamiltonian is generally sub-optimal. We
offer a superior alternative.
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