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

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

2008-05-08

arxiv.org/abs/0805.1214v1

Phys. Rev. A 80, 052334 (2009)

Physics

Quantum Physics

6 pages, 2 figures

Scientific paper

10.1103/PhysRevA.80.052334

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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