Simulation of Many-Body Fermi Systems on a Universal Quantum Computer

@article{Abrams1997SimulationOM,
  title={Simulation of Many-Body Fermi Systems on a Universal Quantum Computer},
  author={Daniel S. Abrams and Seth Lloyd Dept. of Physics and Massachusetts Institute of Technology Department of Mechanical Engineering and Massachusetts Institute of Technology},
  journal={Physical Review Letters},
  year={1997},
  volume={79},
  pages={2586-2589}
}
We provide fast algorithms for simulating many body Fermi systems on a universal quantum computer. Both first and second quantized descriptions are considered, and the relative computational complexities are determined in each case. In order to accommodate fermions using a first quantized Hamiltonian, an efficient quantum algorithm for anti-symmetrization is given. Finally, a simulation of the Hubbard model is discussed in detail. 
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