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...
| Authors: | ; ; ; |
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| Format: | Article |
| Status: | Published version |
| Publication date: | 2011 |
| Country: | España |
| Institution: | Universitat Pompeu Fabra |
| Repository: | Repositorio Digital de la UPF |
| OAI Identifier: | oai:repositori.upf.edu:10230/71752 |
| Online Access: | http://hdl.handle.net/10230/71752 http://dx.doi.org/10.1088/1367-2630/13/9/093021 |
| Access Level: | Open access |
| Keyword: | Algorismes Computació quàntica Física |
| Summary: | 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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