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We study how much noise can be tolerated by a universal gate set before itloses its quantum-computational power. Specifically we look at circuits withperfect stabilizer operations in addition to imperfect non-stabilizer gates. Weprove that for all unitary single-qubit gates there exists a tight depolarizingnoise threshold that determines whether the gate enables universal quantumcomputation or if the gate can be simulated by a mixture of Clifford gates.This exact threshold is determined by the Clifford polytope spanned by the 24single-qubit Clifford gates. The result is in contrast to the situation whereinnon-stabilizer qubit states are used; the thresholds in that case are notcurrently known to be tight.

Tight Noise Thresholds for Quantum Computation with Perfect Stabilizer Operations