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: | ; ; ; |
|---|---|
| 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 |
| _version_ | 1878730218284253184 |
|---|---|
| author | Cuevas, Gemma de las |
| author2 | Dür, Wolfgang Van den Nest, Maarten Martin-Delgado, Miguel Ángel |
| author2_role | author author author |
| author_browse | Cuevas, Gemma de las Dür, Wolfgang Martin-Delgado, Miguel Ángel Van den Nest, Maarten |
| author_facet | Cuevas, Gemma de las Dür, Wolfgang Van den Nest, Maarten Martin-Delgado, Miguel Ángel |
| author_role | author |
| collection | Repositorio Digital de la UPF |
| description | 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. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_17e0bf7dc400a3fc82c56e17bbd0731c |
| institution | Universitat Pompeu Fabra |
| instname_str | Universitat Pompeu Fabra |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:repositori.upf.edu:10230/71752 |
| publishDate | 2011 |
| publishDateSort | 2011 |
| publisher | IOP Publishing |
| publisherStr | IOP Publishing |
| reponame_str | Repositorio Digital de la UPF |
| spelling | Quantum algorithms for classical lattice models Cuevas, Gemma de las Dür, Wolfgang Van den Nest, Maarten Martin-Delgado, Miguel Ángel Algorismes Computació quàntica Física 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. IOP Publishing http://hdl.handle.net/10230/71752 http://dx.doi.org/10.1088/1367-2630/13/9/093021 |
| spellingShingle | Quantum algorithms for classical lattice models Cuevas, Gemma de las Algorismes Computació quàntica Física |
| status_str | publishedVersion |
| title | Quantum algorithms for classical lattice models |
| title_full | Quantum algorithms for classical lattice models |
| title_fullStr | Quantum algorithms for classical lattice models |
| title_full_unstemmed | Quantum algorithms for classical lattice models |
| title_short | Quantum algorithms for classical lattice models |
| title_sort | Quantum algorithms for classical lattice models |
| topic | Algorismes Computació quàntica Física |
| topic_facet | Algorismes Computació quàntica Física |
| url | http://hdl.handle.net/10230/71752 http://dx.doi.org/10.1088/1367-2630/13/9/093021 |