Upper bounds on the noise threshold for fault-tolerant quantum computing (pp0361-0376)
          Julia Kempe, Oder Regev, Falk Unger, and Ronald de Wolf
          doi: https://doi.org/10.26421/QIC10.5-6-1
Abstracts: We prove new upper bounds on the tolerable level of noise in a quantum circuit. We consider circuits consisting of unitary k-qubit gates each of whose input wires is subject to depolarizing noise of strength p, as well as arbitrary one-qubit gates that are essentially noise-free. 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 two-qubit CNOT gate, then our bound becomes 29.3%. These bounds on p are numerically 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, in which the effects of depolarizing noise are very easy to describe.
Key words:  fault-tolerance threshold, noisy quantum computation