Quantum algorithms for classical lattice models
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 Z2 lattice gauge theory on a 3D s...
| Autores: | , , , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2011 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositório: | Docta Complutense |
| Idioma: | inglês |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/42823 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/42823 |
| Access Level: | Acceso aberto |
| Palavra-chave: | 53 Partition-function Computational-complexity. Física-Modelos matemáticos |
| Resumo: | 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 Z2 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. |
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