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We establish concrete criteria for fully supported absolutely continuousspectrum for ergodic CMV matrices and purely absolutely continuous spectrum forlimit-periodic CMV matrices. We proceed by proving several variationalestimates on the measure of the spectrum and the vanishing set of the Lyapunovexponent for CMV matrices, which represent CMV analogues of results obtainedfor Schr\"odinger operators due to Y.\ Last in the early 1990s. Having done so,we combine those estimates with results from inverse spectral theory to obtainpurely absolutely continuous spectrum.

Spectral Approximation for Ergodic CMV Operators with an Application to Quantum Walks