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Upper Bounds on the Noise Threshold for Faulttolerant Quantum Computing
, 2008
"... We prove new upper bounds on the tolerable level of noise in a quantum circuit. We consider circuits consisting of unitary kqubit gates each of whose input wires is subject to depolarizing noise of strength p, as well as arbitrary onequbit gates that are essentially noisefree. We assume that the ..."
Abstract

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We prove new upper bounds on the tolerable level of noise in a quantum circuit. We consider circuits consisting of unitary kqubit gates each of whose input wires is subject to depolarizing noise of strength p, as well as arbitrary onequbit gates that are essentially noisefree. We assume that the output of the circuit is the result of measuring some designated qubit in the final state. Our main result is that for p> 1 − Θ(1 / √ k), the output of any such circuit of large enough depth is essentially independent of its input, thereby making the circuit useless. For the important special case of k = 2, our bound is p> 35.7%. Moreover, if the only allowed gate on more than one qubit is the twoqubit CNOT gate, then our bound becomes 29.3%. These bounds on p are notably better than previous bounds, yet are incomparable because of the somewhat different circuit model that we are using. Our main technique is the use of a Pauli basis decomposition, which we believe should lead to further progress in deriving such bounds. 1