Quantum algorithms for classical lattice models

Autor:	Cuevas, G. De las, Dür, W., Nest, M. Van den, Martin-Delgado, M. A.
Rok vydání:	2011
Předmět:	Quantum Physics Condensed Matter - Statistical Mechanics High Energy Physics - Lattice High Energy Physics - Theory
Zdroj:	New J.Phys.13:093021,2011
Druh dokumentu:	Working Paper
DOI:	10.1088/1367-2630/13/9/093021
Popis:	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. Comment: 21 pages, 12 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1104.2517 Zobrazit plný text záznamu View this record from Arxiv