  It is known that secondary non-stoquastic drivers may offer speed-ups or
catalysis in some models of adiabatic quantum computation accompanying the more
typical transverse field driver. Their combined intent is to raze potential
barriers to zero during adiabatic evolution from a false vacuum to a true
minimum; first order phase transitions are softened into second order
transitions. We move beyond mean-field analysis to a fully quantum model of a
spin ensemble undergoing adiabatic evolution in which the spins are mapped to a
variable mass particle in a continuous one-dimensional potential. We
demonstrate the necessary criteria for enhanced mobility or `speed-up' across
potential barriers is actually a quantum form of the Rayleigh criterion.
Quantum catalysis is exhibited in models where previously thought not possible,
when barriers cannot be eliminated. For the $3$-spin model with secondary
anti-ferromagnetic driver, catalysed time complexity scales between linear and
quadratically with the number of qubits. As a corollary, we identify a useful
resonance criterion for quantum phase transition that differs from the
classical one, but converges on it, in the thermodynamic limit.
