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

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 antisymmetrization is given. Finally, a simulation of the Hubbard model is discussed in detail.