  We show in detail how the Jordan-Wigner transformation can be used to
simulate any fermionic many-body Hamiltonian on a quantum computer. We develop
an algorithm based on appropriate qubit gates that takes a general fermionic
Hamiltonian, written as products of a given number of creation and annihilation
operators, as input. To demonstrate the applicability of the algorithm, we
calculate eigenvalues and eigenvectors of two model Hamiltonians, the
well-known Hubbard model and a generalized pairing Hamiltonian. Extensions to
other systems are discussed.
