Quantum Simulation of SU(3) Lattice Yang-Mills Theory at Leading Order in Large- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>N</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> Expansion