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oai:recercat.cat:10230/717522025-11-05T18:54:22Zcom_2072_6col_2072_452952

Quantum algorithms for classical lattice models Cuevas, Gemma de las Dür, W. Van den Nest, M. 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. 2025-11-04T06:47:41Z 2025-11-04T06:47:41Z 2011 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion de las Cuevas G, Dür W, Van den Nest M, Martin-Delgado MA. Quantum algorithms for classical lattice models. New J Phys. 2011 Sep 9;13(9):093021. DOI: 10.1088/1367-2630/13/9/093021 1367-2630 http://hdl.handle.net/10230/71752 http://dx.doi.org/10.1088/1367-2630/13/9/093021 http://hdl.handle.net/10230/71752 eng New Journal of Physics. 2011 Sep 9;13(9):093021 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Published under a CC BY (Creative Commons Attribution) licence. http://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess application/pdf application/pdf IOP Publishing