Quantum Alternating Operator Ansatz (QAOA) performance regimes for continuous schedules*

The Quantum Approximate Optimization Algorithm and its generalization to Quantum Alternating Operator Ansatze (QAOA) are promising approaches for using quantum computers to tackle challenging problems in combinatorial optimization and beyond. For the setting of easier-to-optimize parameter sequences derived from continuous schedules such as linear ramps, QAOA performance diagrams capture the algorithm's varying performance over starkly different parameter regimes, and yet display qualitatively similar behavior across different target performance metrics and different application domains. In our work, we characterize and explain this observed universal behavior by elucidating the underlying mechanisms, which include the discrete adiabatic theorem, the magnitude of p controlling diabatic transitions at avoided crossings, small-parameter approximations, and holonomies due to changing eigenvector connections. Our results complement and generalize the insights obtained from the usual (continuous) adiabatic perspective. In contrast, we highlight that comparable performance to that of high-depth circuits can be achieved with smaller depth for suitably chosen (somewhat larger) parameters. Furthermore, we outline how our analysis could inform the design of protocols requiring fewer resources and constraints on the mixer than the standard approach to obtain comparable performance.