Quantum algorithms for classical lattice models
Gemma De las Cuevas, Wolfgang Dür, M Van den Nest, M A Martin-Delgado · New Journal of Physics · 2011
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 3D 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 by Van den Nest et al (2009 Phys.Rev. A 80 052334) and extended here.