  We examine the problem of simulating lattice gauge theories on a universal
quantum computer. The basic strategy of our approach is to transcribe lattice
gauge theories in the Hamiltonian formulation into a Hamiltonian involving only
Pauli spin operators such that the simulation can be performed on a quantum
computer using only one and two qubit manipulations. We examine three models,
the U(1), SU(2), and SU(3) lattice gauge theories which are transcribed into a
spin Hamiltonian up to a cutoff in the Hilbert space of the gauge fields on the
lattice. The number of qubits required for storing a particular state is found
to have a linear dependence with the total number of lattice sites. The number
of qubit operations required for performing the time evolution corresponding to
the Hamiltonian is found to be between a linear to quadratic function of the
number of lattice sites, depending on the arrangement of qubits in the quantum
computer. We remark that our results may also be easily generalized to higher
SU(N) gauge theories.
