Tight noise thresholds for quantum computation with perfect stabilizer operations

Physical Review Letters 103, 170504

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W van Dam, M Howard

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We study how much noise can be tolerated by a universal gate set before it loses its quantum-computational power. Specifically we look at circuits with perfect stabilizer operations in addition to imperfect nonstabilizer gates. We prove that for all unitary single-qubit gates there exists a tight depolarizing noise threshold that determines whether the gate enables universal quantum computation 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 24 single-qubit Clifford gates. The result is in contrast to the situation wherein nonstabilizer qubit states are used; the thresholds in that case are not currently known to be tight.