  We introduce a protocol for the fast simulation of $n$-dimensional quantum
systems on $n$-qubit quantum computers with tunable couplings. A mapping is
given between the control parameters of the quantum computer and the matrix
elements of $H_{\rm s}(t)$, an arbitrary, real, time-dependent $n\times n$
dimensional Hamiltonian that is simulated in the $n$-dimensional `single
excitation' subspace of the quantum computer. A time-dependent energy/time
rescaling minimizes the simulation time on hardware having a fixed coherence
time. We demonstrate how three tunably coupled phase qubits simulate a
three-channel molecular collision using this protocol, then study the
simulation's fidelity as a function of total simulation time.
