real_fourier_stf_signal

Graph.real_fourier_stf_signal(duration, initial_coefficient_lower_bound=-1, initial_coefficient_upper_bound=1, fixed_frequencies=None, optimizable_frequency_count=None, randomized_frequency_count=None)

Create a real sampleable signal constructed from Fourier components.

Use this function to create a signal defined in terms of Fourier (sine/cosine) basis signals that can be optimized by varying their coefficients and, optionally, their frequencies.

Parameters

  • duration (float) – The total duration τ\tau of the signal.
  • initial_coefficient_lower_bound (float , optional) – The lower bound cminc_\mathrm{min} on the initial coefficient values. Defaults to -1.
  • initial_coefficient_upper_bound (float , optional) – The upper bound cmaxc_\mathrm{max} on the initial coefficient values. Defaults to 1.
  • fixed_frequencies (np.ndarray or None , optional) – A 1D array containing the fixed non-zero frequencies {fm}\{f_m\} to use for the Fourier basis. If provided, must be non-empty and specified in the inverse units of duration (for example if duration is in seconds, these values must be given in Hertz).
  • optimizable_frequency_count (int or None , optional) – The number of non-zero frequencies MM to use, if the frequencies can be optimized. Defaults to 0.
  • randomized_frequency_count (int or None , optional) – The number of non-zero frequencies MM to use, if the frequencies are to be randomized but fixed. Defaults to 0.

Returns

The optimizable, real-valued, sampleable signal built from the appropriate Fourier components.

Return type

Stf

WARNING

You must provide exactly one of fixed_frequencies, optimizable_frequency_count, or randomized_frequency_count.

SEE ALSO

Graph.real_fourier_pwc_signal : Corresponding operation for Pwc.

Notes

This function sets the basis signal frequencies {fm}\{f_m\} depending on the chosen mode:

  • For fixed frequencies, you provide the frequencies directly.
  • For optimizable frequencies, you provide the number of frequencies MM, and this function creates MM unbounded optimizable variables {fm}\{f_m\}, with initial values in the ranges {[(m1)/τ,m/τ]}\{[(m-1)/\tau, m/\tau]\}.
  • For randomized frequencies, you provide the number of frequencies MM, and this function creates MM randomized constants {fm}\{f_m\} in the ranges {[(m1)/τ,m/τ]}\{[(m-1)/\tau, m/\tau]\}.

After this function creates the MM frequencies {fm}\{f_m\}, it produces the signal

α(t)=v0+m=1M[vmcos(2πtfm)+wmsin(2πtfm)], \alpha^\prime(t) = v_0 + \sum_{m=1}^M [ v_m \cos(2\pi t f_m) + w_m \sin(2\pi t f_m) ],

where {vm,wm}\{v_m,w_m\} are (unbounded) optimizable variables, with initial values bounded by cminc_\mathrm{min} and cmaxc_\mathrm{max}. This function produces the final signal α(t)\alpha(t).

You can use the signals created by this function for chopped random basis (CRAB) optimization 1.

References

[1] P. Doria, T. Calarco, and S. Montangero, Phys. Rev. Lett. 106, 190501 (2011).

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