Monte Carlo Quantum Computing
Abstract
It is shown that a class of separately frustration-free (SFF) Hamiltonians can be Monte Carlo simulated efficiently on a classical computing machine, because such an SFF Hamiltonian corresponds to a Gibbs wavefunction whose nodal structure is efficiently computable by solving a small subsystem associated with a low-dimensional configuration subspace. It is further demonstrated that SFF Hamiltonians can be designed to implement universal ground state quantum computation. The two results combined have effectively solved the notorious sign problem in Monte Carlo simulations, and proved that all bounded-error quantum polynomial time algorithms admit bounded-error probabilistic polynomial time simulations.
Cite
@article{arxiv.2012.14523,
title = {Monte Carlo Quantum Computing},
author = {David H. Wei},
journal= {arXiv preprint arXiv:2012.14523},
year = {2021}
}
Comments
119 pages, 6 figures; broadened the notion of a strongly frustration-free Hamiltonian to a more general concept of separately frustration-free (SFF) Hamiltonian