title: Tight noise thresholds for quantum computation with perfect stabilizer operations.
abstract: 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.
authors.affiliation: Department of Computer Science, University of California, Santa Barbara, California 93106, USA. vandam@cs.ucsb.edu
authors.forename: Wim
authors.initials: W
authors.lastname: van Dam
authors.forename: Mark
authors.initials: M
authors.lastname: Howard