Best I can tell as a non expert is that QC has to assume some underlying "free" sampling operation from wave function collapse (or "branching" if you're a multiverser, though the distinction eludes me) to provide a fundamental speedup. If the waveform just entangles with the detector which is the simplest explanation, then you'll have to run a gradient descent on multiple quantum calculations to find an answer. I suspect that will always turn out to be the same O() as just doing the damn thing classically for a given accuracy.