  We investigate the simulation of fermionic systems on a quantum computer. We
show in detail how quantum computers avoid the dynamical sign problem present
in classical simulations of these systems, therefore reducing a problem
believed to be of exponential complexity into one of polynomial complexity. The
key to our demonstration is the spin-particle connection (or generalized
Jordan-Wigner transformation) that allows exact algebraic invertible mappings
of operators with different statistical properties. We give an explicit
implementation of a simple problem using a quantum computer based on standard
qubits.
