paraqeet.signal package¶
Submodules¶
paraqeet.signal.envelopes module¶
Class definition for the Evelopes.
- class paraqeet.signal.envelopes.ConstantEnvelope¶
Bases:
EnvelopeA constant envelope tone with a fixed length.
- _amplitude: Quantity
The amplitude of the envelope.
- _t_final: Quantity
The length in time of the envelope.
- _gradientFunction: 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.
- get_time_gradient(times)¶
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(times)¶
Compute the constant signal envelope at different times.
- Parameters:
times (Array) – One-dimensional vector of timestamps.
- Returns:
Output of the computation.
- Return type:
Array
- Raises:
NotImplementedError – Subclasses derived from this class must implement this method.
- class paraqeet.signal.envelopes.DCRABEnvelope¶
Bases:
EnvelopeCreate a dCRAB pulse envelope.
The dCRAB pulse is given as a sum of sinusoidal components as [Müller2022] $$f(t) = g(t)Big( 1 + sum_{i=1}^{N_c / 2} c_{2i} frac{cos(omega_{2i} t)}{Lambda(t)}
sum_{i = 1} ^ {N_c/2} c_{2i + 1} frac{sin(omega_{2i + 1} t)}{Lambda(t)} Big)$$
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. Adviced 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.
- __init__(amplitude=None, t_final=None, num_components=2, min_frequency=0.0, max_frequency=31.41592653589793, seed=None)¶
- add_new_components(seed=None)¶
Add self._num_components number of new randomized components to the optimization.
- Parameters:
seed (int | None)
- Return type:
None
- get_coefficients_frequencies_and_phases()¶
Return all the coefficients and frequencies used in the CRAB signal.
- Return type:
list[Quantity]
- get_parameters()¶
Return the parameters of the CRAB signal. The parameters are arranged as follows,
[amplitude, t_final, … total_num coefficients …, … total_num frequencies …]
- get_value(t)¶
Compute the CRAB signal.
- Parameters:
t (Array) – One-dimensional vector of timestamps.
- Returns:
Returns a vector CRAB signal.
- Return type:
Array
- remove_small_coefficients(tol=1e-07)¶
Remove coefficients (and corresponding frequencies) that are smaller than a tolerance.
- Parameters:
tol (float)
- Return type:
None
- class paraqeet.signal.envelopes.Envelope¶
Bases:
WaveformClassical Signal Envelope class.
- _amplitude: Quantity
The amplitude of the envelope.
- _t_final: Quantity
The length in time of the envelope.
- _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.
- __init__(amplitude=None, t_final=None)¶
- property amplitude: Quantity¶
Get the amplitude of the system.
- Returns:
Amplitude of the system.
- Return type:
- get_parameters()¶
Get a list of parameters of the envelope.
- Returns:
List of parameters of the envelope.
- Return type:
List[Quantity]
- abstract get_value(times)¶
Compute the output.
- Parameters:
times (Array) – One-dimensional vector of timestamps.
- Returns:
Output of the computation.
- Return type:
Array
- Raises:
NotImplementedError – Subclasses derived from this class must implement this method.
- class paraqeet.signal.envelopes.FlatTopGaussianEnvelope¶
Bases:
EnvelopeA flat-top Gaussian envelope.
- _amplitude: Quantity
The amplitude of the envelope.
- _t_up: Quantity
The start time of constant section of the envelope.
- _t_down: Quantity
The end time of constant section of the envelope.
- _ramp_time: Quantity
The rate of ramp up and ramp down of the envelope.
- _t_final: Quantity
The length in time of the envelope. Used only if any of t_up, t_down, and ramp_time are none.
- _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.
- __init__(amplitude=None, t_up=None, t_down=None, ramp_time=None, t_final=None)¶
- get_parameters()¶
Get all parameters of the system.
- get_time_gradient(times)¶
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(times)¶
Get the output of the device on time stamps.
- Parameters:
times (Array) – One-dimensional vector of timestamps.
- Returns:
Returns the output of the device.
- Return type:
Array
- get_value_and_gradient(times)¶
Return the gradient wrt dimensionless parameters.
- Parameters:
times (Array) – One-dimensional vector of timestamps.
- Returns:
Returns the gradient wrt dimensionless parameters.
- Return type:
Array
- class paraqeet.signal.envelopes.GaussEnvelope¶
Bases:
EnvelopeCreate a simple Gauss envelope.
- _amplitude: Quantity
The amplitude of the envelope.
- _t_final: Quantity
The length in time of the envelope.
- _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.
- get_time_gradient(times)¶
Compute a Gaussian signals time derivative.
- Parameters:
times (Array) – One-dimensional vector of timestamps.
- Returns:
Returns a vector gaussian signals time derivative.
- Return type:
Array
- get_value(times)¶
Compute a Gaussian signal.
- Parameters:
times (Array) – One-dimensional vector of timestamps.
- Returns:
Returns a vector gaussian signal.
- Return type:
Array
- class paraqeet.signal.envelopes.ZeroEnvelope¶
Bases:
ConstantEnvelopeShorthand implentation of a zero signal envelope.
- _amplitude: Quantity
The amplitude of the envelope.
- _t_final: Quantity
The length in time of the envelope.
- _gradientFunction: 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.
- __init__()¶
paraqeet.signal.generator module¶
Class definition of the Generator model.
- class paraqeet.signal.generator.Generator¶
Bases:
Optimizable,DifferentiableSignal generation stack.
Contrary to most quantum simulators, paraqeet includes a detailed simulation of the control stack. Each component in the stack and its functions are simulated individually and combined here.
Example: A local oscillator and arbitrary waveform generator signal are put through via a mixer device to produce an effective modulated signal.
- abstract get_gradient_at_timestep(time)¶
Return array with the gradient of the signal value for one time step.
The result has the shape (p,) where ‘p’ is the parameter index.
- Parameters:
time (Array) – One time stamp.
- Return type:
Array
- abstract get_value(times)¶
Return array with scalar signal value for each time step.
- Parameters:
times (Array) – One-dimensional vector of timestamps.
- Returns:
Returns the scalar signal vector.
- Return type:
Array
paraqeet.signal.iq_mixer module¶
Class definition for the Sinusoidal generator model.
- class paraqeet.signal.iq_mixer.IQMixer¶
Bases:
GeneratorControl signal generation.
Waveforms of envelopes (low bandwith) are mixed with a local oscillator (high bandwidth) to apply a desired control field to the system.
- Parameters:
- __init__(envelopes, frequency=None, phase=None)¶
- get_gradient_at_timestep(time)¶
Return the gradients from all devices at the given time.
Since the
\[\begin{split}signal = \\Re(\\epsilon(t)^* \\exp(i \\omega t) \\exp(-i \\phi))\end{split}\]Derivative of the signal wrt optimizable parameter of envelope would be
\[\begin{split}0.5 * \\Re(\\partial \\epsilon(t)^* \\exp(i \\omega t) \\exp(-i \\phi))\end{split}\](TODO - Check the envelope derivatives)
And derivative of signal wrt parameter of LO would be
\[\begin{split}0.5 i t \\epsilon(t)^* \\exp(i \\omega t) \\exp(-i \\phi))\end{split}\]And derivative of signal wrt phase would be
\[\begin{split}-0.5 i \\epsilon(t)^* \\exp(i \\omega t) \\exp(-i \\phi))\end{split}\]The 0.5 are due to the Wirtinger derivatives due to Re part.
- Parameters:
time (Array) – Single timestamp.
- Returns:
Return the gradients from all devices at one time.
- Return type:
Array
- get_parameters()¶
Return a list of parameters.
Collects and returns a list of parameters from the tone, generator and the carrier signal.
- Returns:
All Parameters describing the signal.
- Return type:
list[Quantity]
- get_value(times)¶
Generate a signal for time(s).
- Parameters:
t (Array) – One-dimensional vector of timestamps.
times (Array | float)
- Returns:
Returns the signal vector.
- Return type:
Array
- get_value_and_gradient(times)¶
Collect and returns the gradients from all devices.
Since the
\[\begin{split}signal = \\Re(\\epsilon(t)^* \\exp(i \\omega t) \\exp(-i \\phi))\end{split}\]Derivative of the signal wrt optimizable parameter of envelope would be
\[\begin{split}0.5 * \\Re(\\partial \\epsilon(t)^* \\exp(i \\omega t) \\exp(-i \\phi))\end{split}\](TODO - Check the envelope derivatives)
And derivative of signal wrt parameter of LO would be
\[\begin{split}0.5 i t \\epsilon(t)^* \\exp(i \\omega t) \\exp(-i \\phi))\end{split}\]And derivative of signal wrt phase would be
\[\begin{split}-0.5 i \\epsilon(t)^* \\exp(i \\omega t) \\exp(-i \\phi))\end{split}\]The 0.5 are due to the Wirtinger derivatives due to Re part.
- Parameters:
t (Array) – One-dimensional vector of timestamps.
- Returns:
Returns the signal gradient vector.
- Return type:
Array
paraqeet.signal.pwc_generator module¶
- class paraqeet.signal.pwc_generator.PWCGenerator¶
Bases:
GeneratorConvert a complex envelope to PWC pulse.
This sets the pulse parameters to the tlist points. The gradient of the pulse wrt the PWC bins is 1 at that time point and zero everywhere else.
This Generator doesn’t add the LO signal to the envelope pulse. Driving with a PWC pulse (without the LO) is usually done in the rotating frame of drive.
This Generator converts the input complex pulse to the ‘in-phase’ and ‘out-of-phase’ components. This naming convention is used by following [Krantz2019]. In the literature of signal processing these are also called ‘in-phase’ and ‘quadrature’ components (refer to https://en.wikipedia.org/wiki/In-phase_and_quadrature_components).
[Krantz2019] Krantz et al., “A Quantum Engineer’s Guide to Superconducting Qubits.” Applied Physics Reviews 6(2019).
- _envs: list[Waveform]
List of Envelopes
- _tlist: Array
Left time points for discretization. These can be used for propagation and optimization.
- _time_grid: Array
Time grid used to discretize the pulse. These are shifted from tlist by dt, and doesn’t include zero time.
- _max_amplitude: float
Maximum amplitude of the drive
- _inphase: Quantity
The in-phase component of the pulse
- _outofphase: Quantity
The out-of-phase component of the pulse
- _optimizable_paramters: list[Quantity]
List of own parameters that would be optimized by the optimizer.
- _multiply_flat_top: bool
Flag to multiply flat-top-Gaussain pulse to the signal to ensure it starts and ends at zero.
- Parameters:
envelopes (List[Waveform]) – List of input devices.
- __init__(envelopes, tlist, max_amplitude=None)¶
- Parameters:
envelopes (list[Waveform] | None)
tlist (Array)
max_amplitude (float | None)
- property envs: list[Waveform]¶
Gets the list of envelopes.
- Returns:
The list of waveforms associated with the generator.
- Return type:
list[Waveform]
- get_gradient_at_timestep(time)¶
Return signal gradient wrt inphase and out-of-phase.
This returns a list of ones as the gradient of the envelope wrt a step is 1 for that time bin and 0 everywhere else.
- Parameters:
time (Array) – One time step.
- Returns:
PWC signal gradients.
- Return type:
Array
- get_number_of_pwc_pixels()¶
Return number of PWC pixels generated by the PWC generator.
- Return type:
int
- get_parameters()¶
Return a list of parameters.
Return the inphase and out-of-phase as parameters.
- Returns:
All Parameters describing the signal.
- Return type:
list[Quantity]
- get_value(times)¶
Generate the PWC signal for time(s) ‘t’.
- Parameters:
times (Array) – One-dimensional vector of timestamps.
- Returns:
Returns the signal vector.
- Return type:
Array
- get_value_and_gradient(times)¶
Return signal gradient wrt inphase and out-of-phase.
This returns a list of ones as the gradient of the envelope wrt a step is 1 for that time bin and 0 everywhere else.
- Parameters:
times (Array) – Array of time steps.
- Returns:
PWC signal gradients.
- Return type:
Array
- property max_amplitude: float¶
Get the maximum drive amplitude.
- Return type:
The value of the maximum drive amplitude.
- property multiply_flat_top: bool¶
Flag to multiply the pulse with a FlatTop.
This can be used to make the start and end values zeros and force the PWC pulse to change smoothly.
- Returns:
multiply_flat_top – Flag value for multiply_flat_top.
- Return type:
bool
- set_optimizable_parameters(params)¶
Set specified parameters to be optimized.
Optimizable paramters can be inphase and out-of-phase.
- Parameters:
params (list[Quantity])
- Return type:
None
- property tlist: Array¶
Get time grid discritization for generating PWC pulse.
- Returns:
Array of time points at which envelope is discritized.
- Return type:
Array
paraqeet.signal.waveform module¶
Class definition for the Device model.
- class paraqeet.signal.waveform.DRAGMixer¶
Bases:
WaveformA DRAG mixed waveform signal.
The DRAG component is calculated for a set of envelopes and added in orthogonal direction in the x-y plane.
- _envs: list[Envelope]
The list of shape defining signal envelops.
- _deltas: list[Quantity]
The delta parameter by which to shift the frequency of the DRAG component.
- __init__(envelopes, deltas=None)¶
- get_parameters()¶
Return a list of parameters.
Collects and returns a list of parameters from the tone, generator and the carrier signal.
- Returns:
All Parameters describing the signal.
- Return type:
list[Quantity]
- get_value(times)¶
Evaluate a carrier signal from an input time vector.
- Parameters:
t (Array) – One-dimensional vector of timestamps.
times (Array | float)
- Returns:
Returns a vector carrier signal.
- Return type:
Array
- get_value_and_gradient(times)¶
Generate gradient of the signal for an array of time.
Collect and return the parameter gradients from the Tone and the carrier Tone. Compute the gradient of the generator parameters by AD. The order of the gradients should match the order of paramters in self.get_parameter() method
- Parameters:
times (Array) – An array of time points.
- Returns:
Array of gradients wrt each parameter for each time point.
- Return type:
Array
- class paraqeet.signal.waveform.FlatTopGaussianFilter¶
Bases:
WaveformA shape filter that forces the pulse to smoothly start and end at zero. This filter multiplies the input pulse with a flat-top Gaussian pulse.
Note - Use filters before the generators. Else Automatic differentiation does not work.
This is similar to PWCGenerator.multiply_flat_top = True.
- get_parameters()¶
Return a list of parameters.
Collects and returns a list of parameters from the tone, generator and the carrier signal.
- Returns:
All Parameters describing the signal.
- Return type:
list[Quantity]
- get_value(times)¶
Evaluate a carrier signal from an input time vector.
- Parameters:
times (Array) – One-dimensional vector of timestamps.
- Returns:
Returns a vector carrier signal.
- Return type:
Array
- get_value_and_gradient(times)¶
Generate gradient of the signal for an array of time.
Collect and return the parameter gradients from the Tone and the carrier Tone. Compute the gradient of the generator parameters by AD. The order of the gradients should match the order of paramters in self.get_parameter() method
- Parameters:
times (Array) – An array of time points.
- Returns:
Array of gradients wrt each parameter for each time point.
- Return type:
Array
- class paraqeet.signal.waveform.LocalOscillator¶
Bases:
WaveformA local oscillators carrier signal.
- _lo_freqQuantity
The frequency of the carrier signal.
- property frequency: Quantity¶
Get The frequency of the constant oscillating tone.
- Returns:
The frequency of the tone.
- Return type:
- get_parameters()¶
Return device parameters.
- Returns:
Returns the carrier signal frequency.
- Return type:
list[Quantity]
- get_time_gradient(times)¶
Compute a signals time derivative.
- Parameters:
times (Array) – One-dimensional vector of timestamps.
- Returns:
Returns a vector signals time derivative.
- Return type:
Array or JitWrapped
- get_value(times)¶
Evaluate a carrier signal from an input time vector.
- Parameters:
times (Array) – One-dimensional vector of timestamps.
- Returns:
Returns a vector carrier signal.
- Return type:
Array
- get_value_and_gradient(times)¶
Return the gradient wrt to frequency of carrier signal.
- Parameters:
times (Array) – Array of time points to evaluate gradients at.
- Returns:
Gradient of tone wrt to frequency.
- Return type:
Array
- class paraqeet.signal.waveform.Waveform¶
Bases:
Optimizable,DifferentiableClassical electronics.
- get_time_and_parameter_gradient(times)¶
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)¶
Compute a signal envelopes time derivative.
- Parameters:
times (Array) – One-dimensional vector of timestamps.
- Returns:
Returns a vector signals time derivative.
- Return type:
Array
- abstract get_value(times)¶
Compute the output.
- Parameters:
times (Array) – One-dimensional vector of timestamps or a single value.
- Returns:
Output of the computation.
- Return type:
Array
- get_value_and_gradient(times)¶
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
Module contents¶
Signal generation model module.