Degeneracy in analog processor (e.g., quantum processor) operation is mitigated via use of floppy qubits or domains of floppy qubits (i.e., qubit(s) for which the state can be flipped with no change in energy), which can significantly boost hardware performance on certain problems, as well as improve hardware performance for more general problem sets. Samples are drawn from an analog processor, and devices comprising the analog processor evaluated for floppiness. A normalized floppiness metric is calculated, and an offset added to advance the device in annealing. Degeneracy in a hybrid computing system that comprises a quantum processor is mitigated by determining a magnetic susceptibility of a qubit, and tuning a tunneling rate for the qubit based on a tunneling rate offset determined based on the magnetic susceptibility. Quantum annealing evolution is controlled by causing the evolution to pause for a determined pause duration.