Behavioural randomized controlled trials (RCTs) are the empirical workhorse of behavioural science, yet quantum computing has reached the field only through opinion-dynamics demonstrations and decision-theory formalism, leaving the RCT analysis pipeline unexamined. I ask, stage by stage, where quantum or quantum-like computation earns its place against a strong classical baseline, and report three controlled simulation pilots across the pipeline. In a power-calculation pilot anchored on a 97-outcome preprocessing multiverse of real behavioural RCTs, quantum amplitude estimation recovers enumerated multiverse-significance fractions with absolute error 20-30 times smaller than classical sampled Monte Carlo at matched query budgets on the two non-degenerate outcomes, conditional on efficient state preparation. In an interference pilot, an entanglement-structured estimator recovers a four-way spillover that a pairwise model cannot represent at any sample size. In an adaptation pilot, a quantum-inspired contextual bandit is decisively beaten by a correctly specified classical baseline. The three results - one conditional win, one representational win, one honest loss - yield a decision rule for when quantum methods are worth adopting, piloting, or deferring, together with a five-gap research agenda.

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