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 |