  We show that quantum circuits cannot be made fault-tolerant against a
depolarizing noise level of approximately 45%, thereby improving on a previous
bound of 50% (due to Razborov). Our precise quantum circuit model enables
perfect gates from the Clifford group (CNOT, Hadamard, S, X, Y, Z) and
arbitrary additional one-qubit gates that are subject to that much depolarizing
noise. We prove that this set of gates cannot be universal for arbitrary (even
classical) computation, from which the upper bound on the noise threshold for
fault-tolerant quantum computation follows.
