Quantum algorithms for spin models and simulable gate sets for quantum computation
Abstract
We present elementary mappings between classical lattice models and quantum circuits. These mappings provide a general framework to obtain efficiently simulable quantum gate sets from exactly solvable classical models. For example, we recover and generalize the simulability of Valiant's match-gates by invoking the solvability of the free-fermion eight-vertex model. Our mappings furthermore provide a systematic formalism to obtain simple quantum algorithms to approximate partition functions of lattice models in certain complex-parameter regimes. For example, we present an efficient quantum algorithm for the six-vertex model as well as a 2D Ising-type model. We finally show that simulating our quantum algorithms on a classical computer is as hard as simulating universal quantum computation (i.e. BQP-complete).
Cite
@article{arxiv.0805.1214,
title = {Quantum algorithms for spin models and simulable gate sets for quantum computation},
author = {M. Van den Nest and W. Dür and R. Raussendorf and H. J. Briegel},
journal= {arXiv preprint arXiv:0805.1214},
year = {2012}
}
Comments
6 pages, 2 figures