Publication: Quantum algorithms for classical lattice models
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2011-09-09
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IOP Publishing
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Abstract
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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© 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.