### 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) |
---|---|

Pages (from-to) | 361-376 |

Number of pages | 16 |

Journal | Quantum Information and Computation |

Volume | 10 |

Issue number | 5-6 |

State | Published - May 1 2010 |

### Fingerprint

### Keywords

- Fault-tolerance threshold
- Noisy quantum computation

### ASJC Scopus subject areas

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

### Cite this

*Quantum Information and Computation*,

*10*(5-6), 361-376.

**Upper bounds on the noise threshold for fault-tolerant quantum computing.** / Kempe, Julia; Regev, Oded; Unger, Falk; de Wolf, Ronald.

Research output: Contribution to journal › Article

*Quantum Information and Computation*, vol. 10, no. 5-6, pp. 361-376.

}

TY - JOUR

T1 - Upper bounds on the noise threshold for fault-tolerant quantum computing

AU - Kempe, Julia

AU - Regev, Oded

AU - Unger, Falk

AU - de Wolf, Ronald

PY - 2010/5/1

Y1 - 2010/5/1

N2 - 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.

AB - 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.

KW - Fault-tolerance threshold

KW - Noisy quantum computation

UR - http://www.scopus.com/inward/record.url?scp=77953940472&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77953940472&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:77953940472

VL - 10

SP - 361

EP - 376

JO - Quantum Information and Computation

JF - Quantum Information and Computation

SN - 1533-7146

IS - 5-6

ER -