paraqeet.signal.envelopes.DCRABEnvelope#
- class paraqeet.signal.envelopes.DCRABEnvelope(amplitude=None, t_final=None, num_components=2, min_frequency=0.0, max_frequency=31.41592653589793, seed=None)[source]#
Bases:
EnvelopeCreate a dCRAB pulse envelope.
The dCRAB pulse is given as a sum of sinusoidal components as [Müller2022]
\[f(t) = g(t)( 1 + \sum_{i=1}^{N_c / 2} c_{2i} \frac{\cos(\omega_{2i} t)}{\Lambda(t)} + \sum_{i = 1} ^ {N_c/2} c_{2i + 1} \frac{\sin(\omega_{2i + 1} t)}{\Lambda(t)} )\]Here we consider \(g(t) = \Lambda(t) = 1\) for simplicity. Further, even components are for cosine and odd components are for sine. Note - The function is designed to work well for even total number of components. For odd total number it may not work as expected.
[Müller2022] Müller et al. “One decade of quantum optimal control in the chopped random basis”
- _amplitude: Quantity
The amplitude of the envelope.
- _t_final: Quantity
The length in time of the envelope.
- _num_components: int
Number of components added each iteration to the dCRAB basis. Defaults to 2. Advised to be an even number.
- _total_num_components: int
Total number of components in the current dCRAB basis. This is the number of coefficients or the number of frequencies present. NOT the sum of them.
- _real_coefficients: list[Quantity]
Vector quantity as a list of amplitudes of individual sinusoidal components.
- _real_frequencies: list[Quantity]
Vector quantity as a list of frequencies of individual sinusoidal components.
- _real_phases: list[Quantity]
Vector quantity as a list of phases of individual sinusoidal components.
- _gradient_function: Callable | None
The function to calculate the gradient with respect to a set of previously defined parameters.
- _grad_arg_nums: tuple[int, …]
The identifying indices of which parameters to calculate the gradient with respect to.
- Parameters:
- __init__(amplitude=None, t_final=None, num_components=2, min_frequency=0.0, max_frequency=31.41592653589793, seed=None)[source]#
Methods
__init__([amplitude, t_final, ...])add_new_components([seed])Add self._num_components number of new randomized components to the optimization.
Return all the coefficients and frequencies used in the CRAB signal.
Return the parameters of the CRAB signal.
Compute the double derivative with respect to parameter and time.
get_time_gradient(times)Compute a signal envelopes time derivative.
get_value(t)Compute the CRAB signal.
get_value_and_gradient(times)Compute the gradient of the _evaluate method.
remove_small_coefficients([tol])Remove coefficients (and corresponding frequencies) that are smaller than a tolerance.
set_all_optimizable_parameters(all_params)Set all optimizable parameters in the optimization.
set_optimizable_parameters(params)Set optimizable parameters for optimization.
Attributes
Get the optimizable parameters
Get the amplitude of the system.
Get the name of the parameter.
Get the optimizable parameters
Get the length of the tone.
- add_new_components(seed=None)[source]#
Add self._num_components number of new randomized components to the optimization.
- Parameters:
seed (int | None)
- Return type:
None
- property all_optimizable_parameters: list[Quantity]#
Get the optimizable parameters
- Returns:
The list of all the optimizable parameters considered in the optimization
- Return type:
list[Quantity]
- property amplitude: Quantity#
Get the amplitude of the system.
- Returns:
Amplitude of the system.
- Return type:
- get_coefficients_frequencies_and_phases()[source]#
Return all the coefficients and frequencies used in the CRAB signal.
- Return type:
list[Quantity]
- get_parameters()[source]#
Return the parameters of the CRAB signal.
The parameters are arranged as follows, [amplitude, t_final, … total_num coefficients …, … total_num frequencies …]
- get_time_and_parameter_gradient(times)[source]#
Compute the double derivative with respect to parameter and time.
This function computes $\frac{\partial^2 \Omega}{\partial t \partial alpha}$ for a pulse $\Omega(t)$ and parameter $\alpha$.
- Parameters:
times (Array) – One-dimensional vector of timestamps.
- Returns:
Returns a vector signals time derivative.
- Return type:
Array
- get_time_gradient(times)[source]#
Compute a signal envelopes time derivative.
- Parameters:
times (Array) – One-dimensional vector of timestamps.
- Returns:
Returns a vector signals time derivative.
- Return type:
Array
- get_value(t)[source]#
Compute the CRAB signal.
- Parameters:
t (Array) – One-dimensional vector of timestamps.
- Returns:
Returns a vector CRAB signal.
- Return type:
Array
- get_value_and_gradient(times)[source]#
Compute the gradient of the _evaluate method.
Uses Automatic differentiation as a fallback. The _evaluate method should be a pure function (should take the optimizable parameters as function arguments and doesn’t depend on global variables). Refer to https://jax.readthedocs.io/en/latest/notebooks/Common_Gotchas_in_JAX.html for functionally pure functions. To implement analytical gradients / other methods for gradient computation overwrite this method in the inherited class.
- Parameters:
times (Array) – One-dimensional vector of timestamps.
- Returns:
Returns the gradient array of the _evaluate method.
- Return type:
Array
- property name: str | None#
Get the name of the parameter.
- Returns:
Name of the parameter.
- Return type:
str | None
- property optimizable_parameters: list[Quantity]#
Get the optimizable parameters
- Returns:
The list of optimizable parameters associated with the object.
- Return type:
list[Quantity]
- remove_small_coefficients(tol=1e-07)[source]#
Remove coefficients (and corresponding frequencies) that are smaller than a tolerance.
- Parameters:
tol (float)
- Return type:
None
- set_all_optimizable_parameters(all_params)[source]#
Set all optimizable parameters in the optimization.