  Quantum simulations of the dynamics of QCD have been limited by the
complexities of mapping the continuous gauge fields onto quantum computers. By
parametrizing the gauge invariant Hilbert space in terms of plaquette degrees
of freedom, we show how the Hilbert space and interactions can be expanded in
inverse powers of N_c. At leading order in this expansion, the Hamiltonian
simplifies dramatically, both in the required size of the Hilbert space as well
as the type of interactions involved. Adding a truncation of the resulting
Hilbert space in terms of local energy states we give explicit constructions
that allow simple representations of SU(3) gauge fields on qubits and qutrits.
This formulation allows a simulation of the real time dynamics of a SU(3)
lattice gauge theory on a 5x5 and 8x8 lattice on ibm_torino with a CNOT depth
of 113.
