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

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

Volume | 70 |

Issue number | 6 |

DOIs | |

State | Published - Aug 2004 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

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

*70*(6). https://doi.org/10.1103/PhysRevB.70.064517

**Decoherence in Josephson-junction qubits due to critical-current fluctuations.** / Van Harlingen, D. J.; Robertson, T. L.; Plourde, Britton; Reichardt, P. A.; Crane, T. A.; Clarke, John.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 70, no. 6. https://doi.org/10.1103/PhysRevB.70.064517

}

TY - JOUR

T1 - Decoherence in Josephson-junction qubits due to critical-current fluctuations

AU - Van Harlingen, D. J.

AU - Robertson, T. L.

AU - Plourde, Britton

AU - Reichardt, P. A.

AU - Crane, T. A.

AU - Clarke, John

PY - 2004/8

Y1 - 2004/8

N2 - We compute the decoherence caused by 1/f fluctuations at low frequency f in the critical current I0 of Josephson junctions incorporated into flux, phase, charge, and hybrid flux-charge superconducting quantum bits (qubits). The dephasing time τφ scales as I 0/ΩΛSI01/2 (1 Hz), where Ω/2π is the energy-level splitting frequency, SI0(1 Hz) is the spectral density of the critical-current noise at 1 Hz, and Λ = /I0dΩ/ΩdI0/ 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(-t2/2τφ2) 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 I0 and area A, and show that their values of SI0 (1 Hz) scale to within a factor of 3 of [144(I0/μA) 2/(A/μm2)](pA)2/Hz at 4.2 K. We empirically extrapolate SI01/2 (1 Hz) to lower temperatures using a scaling T(K)/4.2. Using this result, we find that the predicted values of τφ at 100 mK range from 0.8 to 12 μs, and are usually substantially longer than values measured experimentally at lower temperatures.

AB - We compute the decoherence caused by 1/f fluctuations at low frequency f in the critical current I0 of Josephson junctions incorporated into flux, phase, charge, and hybrid flux-charge superconducting quantum bits (qubits). The dephasing time τφ scales as I 0/ΩΛSI01/2 (1 Hz), where Ω/2π is the energy-level splitting frequency, SI0(1 Hz) is the spectral density of the critical-current noise at 1 Hz, and Λ = /I0dΩ/ΩdI0/ 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(-t2/2τφ2) 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 I0 and area A, and show that their values of SI0 (1 Hz) scale to within a factor of 3 of [144(I0/μA) 2/(A/μm2)](pA)2/Hz at 4.2 K. We empirically extrapolate SI01/2 (1 Hz) to lower temperatures using a scaling T(K)/4.2. Using this result, we find that the predicted values of τφ at 100 mK range from 0.8 to 12 μs, and are usually substantially longer than values measured experimentally at lower temperatures.

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U2 - 10.1103/PhysRevB.70.064517

DO - 10.1103/PhysRevB.70.064517

M3 - Article

VL - 70

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 6

ER -