Quantum algorithms for classical lattice models

Details Quantum algorithms for classical lattice models Quantum algorithms for classical lattice models

2011-04-13

arxiv.org/abs/1104.2517v1

New J.Phys.13:093021,2011

Physics

Quantum Physics

21 pages, 12 figures

Scientific paper

10.1088/1367-2630/13/9/093021

We give efficient quantum algorithms to estimate the partition function of (i) the six vertex model on a two-dimensional (2D) square lattice, (ii) the Ising model with magnetic fields on a planar graph, (iii) the Potts model on a quasi 2D square lattice, and (iv) the Z_2 lattice gauge theory on a three-dimensional square lattice. Moreover, we prove that these problems are BQP-complete, that is, that estimating these partition functions is as hard as simulating arbitrary quantum computation. The results are proven for a complex parameter regime of the models. The proofs are based on a mapping relating partition functions to quantum circuits introduced in [Van den Nest et al., Phys. Rev. A 80, 052334 (2009)] and extended here.

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