### Abstract

We compute the decoherence caused by 1/f fluctuations at low frequency f in the critical current I_{0} of Josephson junctions incorporated into flux, phase, charge, and hybrid flux-charge superconducting quantum bits (qubits). The dephasing time τ_{φ} scales as I _{0}/ΩΛS_{I0}^{1/2} (1 Hz), where Ω/2π is the energy-level splitting frequency, S_{I0}(1 Hz) is the spectral density of the critical-current noise at 1 Hz, and Λ = /I_{0}dΩ/ΩdI_{0}/ is a parameter computed for given parameters for each type of qubit that specifies the sensitivity of the level splitting to critical-current fluctuations. Computer simulations show that the envelope of the coherent oscillations of any qubit after time t scales as exp(-t^{2}/2τ_{φ}^{2}) when the dephasing due to critical-current noise dominates the dephasing from all sources of dissipation. We compile published results for fluctuations in the critical current of Josephson tunnel junctions fabricated with different technologies and a wide range in I_{0} and area A, and show that their values of S_{I0} (1 Hz) scale to within a factor of 3 of [144(I_{0}/μA) ^{2}/(A/μm^{2})](pA)^{2}/Hz at 4.2 K. We empirically extrapolate S_{I0}^{1/2} (1 Hz) to lower temperatures using a scaling T(K)/4.2. Using this result, we find that the predicted values of τ_{φ} at 100 mK range from 0.8 to 12 μs, and are usually substantially longer than values measured experimentally at lower temperatures.

Original language | English (US) |
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Pages (from-to) | 064517-1-064517-13 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 70 |

Issue number | 6 |

DOIs | |

State | Published - Aug 1 2004 |

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### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*70*(6), 064517-1-064517-13. https://doi.org/10.1103/PhysRevB.70.064517