New limits on fault-tolerant quantum computation

We show that quantum circuits cannot be made faulttolerant against a depolarizing noise level of \hat \theta= (6 - 2\sqrt 2 )/7 \approx 45%, thereby improving on a previous bound of 50% (due to Razborov [18]). More precisely, the circuit model for which we prove this bound contains perfect gates from the Clifford group (CNOT, Hadamard, S, X, Y , Z) and arbitrary additional one-qubit gates that are subject to depolarizing noise \hat \theta. 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 faulttolerant quantum computation follows.