qtcad.qubit.spectra module

Module introducing pre-defined noise spectra for common types of classical noise.

qtcad.qubit.spectra.lorentz(w, S0, wc, w0=0.0)

Lorentzian spectrum.

Mathematically, the spectrum is defined by

\[S(\omega)=\frac{S_0/\pi\omega_c}{1+[(\omega-\omega_0)/\omega_c]^2},\]

where \(S_0\) is the total noise power, \(\omega_c\) is the cutoff angular frequency (half-width at half maximum), and \(\omega_0\) is the central frequency.

Parameters

• w (ndarray) – the angular frequencies at which the spectrum is evaluated.

• S0 (float) – total noise power.

• wc (float) – cutoff angular frequency (half-width at half maximum).

• w0 (float) – central freqency

Returns

ndarray – The spectrum evaluated at angular frequencies w.

Note

Integrating the spectrum from \(-\infty\) to \(\infty\) yields \(S_0\).

qtcad.qubit.spectra.power_law(w, S0, alpha, w0=0.0)

Power law spectrum.

Mathematically, the spectrum is defined by

\[S(\omega) = \frac{S_0}{(\omega-\omega_0)^\alpha},\]

where \(S_0\) is the noise amplitude, \(\alpha\) is the noise exponent, and \(\omega_0\) is the central frequency.

Parameters

• w (ndarray) – the angular frequencies at which the spectrum is evaluated.

• S0 (float) – Amplitude.

• alpha (float) – Exponent.

• w0 (float) – Central freqency.

Returns

ndarray – The spectrum evaluated at angular frequencies w.