A qubit starts in |0⟩. A sequence of m gates is drawn uniformly at random from the single-qubit Clifford group (24 elements — every rotation of the Bloch sphere that maps its axes onto each other). One final gate, the exact inverse of the whole random sequence, is appended. Noiselessly, this always returns the qubit to |0⟩ regardless of m — but each real gate leaks a little probability into the maximally-mixed state, so the measured "survival probability" P(0) decays with m.
P(m) = A·r^m + B, B = 1/2
average gate error ε = (1 − r) / 2
Because the noise model is averaged ("twirled") over the whole Clifford group, the decay curve depends only on sequence length m — not on which specific random gates were drawn. That is the trick that lets RB extract a single average error rate without ever reconstructing the full noisy process (no tomography needed). Each data point below is the mean survival probability over several random sequences at a given m; more sequences and more measurement shots shrink the scatter and pull the fitted ε toward the true value.
- εtrue — the hidden per-gate error rate this experiment is trying to measure.
- Max sequence length — the longest random-sequence-plus-inverse circuit tried.
- Sequences per run — how many independent random circuits are averaged at each length, per click of "Run Experiment".
- Shots per sequence — how many times each circuit is measured (finite-shot noise is what makes points scatter around the true curve).