Single-Qubit RB: Monte Carlo Survival Probability

Quantum hardware teams cannot simply "look at" a qubit to see how good its gates are — any direct check would need a perfect reference gate, which doesn't exist. Randomized benchmarking sidesteps this by applying long random sequences of Clifford gates followed by the sequence's own exact inverse, so a perfect qubit always returns to where it started; real, noisy hardware falls short by an amount that grows exponentially with sequence length. This simulator runs the real protocol: a genuine 24-element Clifford group acting exactly on the Bloch sphere, real per-gate depolarizing noise, real randomly-sampled measurement shots, and a real least-squares exponential fit that extracts the average gate error rate from the resulting decay curve — nothing here is precomputed or faked.