## Abstract

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 measur√ng 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.

Original language | English (US) |
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Pages (from-to) | 361-376 |

Number of pages | 16 |

Journal | Quantum Information and Computation |

Volume | 10 |

Issue number | 5-6 |

DOIs | |

State | Published - May 1 2010 |

## Keywords

- Fault-tolerance threshold
- Noisy quantum computation

## ASJC Scopus subject areas

- Theoretical Computer Science
- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics
- General Physics and Astronomy
- Computational Theory and Mathematics