RT Journal Article
T1 Quantum algorithms for classical lattice models
A1 De las Cuevas, G.
A1 Dürt, W.
A1 Van den Nest, M.
A1 Martín-Delgado Alcántara, Miguel Ángel
AB 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.
PB IOP Publishing
SN 1367-2630
YR 2011
FD 2011-09-09
LK https://hdl.handle.net/20.500.14352/42823
UL https://hdl.handle.net/20.500.14352/42823
LA eng
NO © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. We thank H J Briegel and J I Cirac for helpful discussions. This work was supported by the FWF and the European Union (QICS, SCALA, NAMEQUAM). MVDN acknowledges support from the excellence cluster MAP. MAMD acknowledges support from the Spanish MICINN grant FIS2009-10061, CAM research consortium QUITEMAD S2009-ESP-1594, European FET-7 grant PICC and UCM-BS grant GICC-910758.
NO Unión Europea. FP7
NO Ministerio de Ciencia e Innovación (MICINN)
NO Comunidad de Madrid
NO Universidad Complutense de Madrid/Banco de Santander
NO FWF
DS Docta Complutense
RD 17 abr 2025