It is known that secondary nonstoquastic drivers may offer speedups 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 that the necessary criterion for enhanced mobility or “speedup” 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 a secondary antiferromagnetic driver, catalyzed time complexity scales between linear and quadratic 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.
American Physical Society