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

@article{Nest2009QuantumAF,
  title={Quantum algorithms for spin models and simulable gate sets for quantum computation},
  author={Maarten Van den Nest and Wolfgang Dur and Robert Raussendorf and Hans J. Briegel},
  journal={Physical Review A},
  year={2009},
  volume={80},
  pages={052334}
}
We present simple mappings between classical lattice models and quantum circuits, which provide a systematic formalism to obtain quantum algorithms to approximate partition functions of lattice models in certain complex-parameter regimes. We, e.g., present an efficient quantum algorithm for the six-vertex model as well as a two-dimensional Ising-type model. We show that classically simulating these (complex-parameter) spin models is as hard as simulating universal quantum computation, i.e., BQP… 

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