Magic State Distillation: Purifying T-Gates for Fault Tolerance

Every fault-tolerant quantum computer needs the non-Clifford T gate to be universal, but T gates can't be protected by stabilizer codes the way Clifford gates can — instead, noisy copies of the "magic state" they consume are purified through distillation circuits. This simulator renders the Bravyi–Kitaev 15-to-1 protocol in 3D: fifteen noisy input states orbit and converge into a single higher-fidelity output state, while live readouts track the error rate collapsing as ε_out ≈ 35·ε_in³ per round, the physical qubit cost climbing as 15 per round, and the net suppression factor achieved after chaining up to three rounds.