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arXiv · 0805.1214

Quantum algorithms for spin models and simulable gate sets for quantum computation

M. Van den Nest·W. Dür·R. Raussendorf·H. J. Briegel
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Abstract

We present elementary mappings between classical lattice models and quantum circuits. These mappings provide a general framework to obtain efficiently simulable quantum gate sets from exactly solvable classical models. For example, we recover and generalize the simulability of Valiant's match-gates by invoking the solvability of the free-fermion eight-vertex model. Our mappings furthermore provide a systematic formalism to obtain simple quantum algorithms to approximate partition functions of lattice models in certain complex-parameter regimes. For example, we present an efficient quantum algorithm for the six-vertex model as well as a 2D Ising-type model. We finally show that simulating our quantum algorithms on a classical computer is as hard as simulating universal quantum computation (i.e. BQP-complete).

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M. Van den Nest, W. Dür, R. Raussendorf, H. J. Briegel. 2008-05-08. Quantum algorithms for spin models and simulable gate sets for quantum computation. https://doi.org/10.1103/physreva.80.052334

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