filter_functions.analytic module

This file provides functions for the analytical solutions to some of the dynamical decoupling sequences. Note that the filter functions given here differ by a factor of 1/omega**2 from those defined in this package due to different conventions. See for example [Cyw08]. Depending on the definition of the noise Hamiltonian one might also get different results. The functions here agree for

\[B_\alpha\equiv\sigma_z/2.\]

Functions

FID(): Free Induction Decay / Ramsey pulse
SE(): Spin Echo
PDD(): Periodic Dynamical Decoupling
CPMG(): Carr-Purcell-Meiboom-Gill Sequence
CDD(): Concatenated Dynamical Decoupling
UDD(): Uhrig Dynamical Decoupling

References

[Cyw08]

Cywiński, Ł., Lutchyn, R. M., Nave, C. P., & Das Sarma, S. (2008). How to enhance dephasing time in superconducting qubits. Physical Review B - Condensed Matter and Materials Physics, 77(17), 1–11. https://doi.org/10.1103/PhysRevB.77.174509

CDD(z, g)[source]

CPMG(z, n)[source]

FID(z)[source]

PDD(z, n)[source]

SE(z)[source]

UDD(z, n)[source]