pygsti.extras.drift.probtrajectory
Functions for Fourier analysis of equally spaced timeseries data
Module Contents
Classes
Encapulates a timedependent probability distribution, as a sum of timedependent basis functions. 

Encapulates a timedependent probability distribution that is actually a constant. 

Encapulates a timedependent probability distribution that is parameterized as a 
Functions

The negative loglikelihood of a ProbTrajectory, modelling a timedependent probability distribution. 

The negative loglikelihood of varying probabilities probs, evaluated for the data streams 

Implements maximum likelihood estimation over a model for a timeresolved probabilities trajectory, 

Reduces the amplitudes in a CosineProbTrajectory model until the model is valid, i.e., all probabilities 
 class pygsti.extras.drift.probtrajectory.ProbTrajectory(outcomes, hyperparameters, parameters)
Bases:
object
Encapulates a timedependent probability distribution, as a sum of timedependent basis functions.
Initializes a ProbTrajectory object.
Parameters
 outcomeslist
What the probability distribution is over. Typically, all possible outcomes for the circuit that this is a probability trajectory for.
 hyperparameterslist
Each derived ProbTrajectory object is intended to encompass a family of parameterized models for a timevarying probability, and this specifies the specific parameterized model in the class. For example, the CosineProbTrajectory object is a derived class whereby each probability is the summation of some number of cosines, and this specifies the number and frequencies of those cosines. The probability trajectory for each outcome is parameterized by a value for each hyperparameter.
 parameters :
A dictonary where the keys are all but the last element of outcomes, and the elements are lists of the same lengths as hyperparameters. These are the parameters of the parameterized model defined by (the derived class) and hyperparameters. The parameter values for the final outcome are assumed to be entirely fixed by the necessity for the probability trajectories to sum to 1 at all times.
Returns
A new ProbTrajectory object.
 copy()
 abstract basisfunction(i, times)
The ith basis function of the model, evaluated at the times in times.
Defined in a derived class
Parameters
 iType specified by derived class.
The basis function specified by the hyperparameter i. This method should expect all possible hyperparameter values (often ints in some range, or a float) as this input
 timeslist
The times to evaluate the basis function at.
Returns
 list
The values of the basis function at the specified times.
 set_hyperparameters(hyperparameters, parameters)
Sets the hyperparameters – i.e., defines a new parameterized model – and the parameters (see init for details).
 set_parameters(parameters)
Sets the parameters of the model (see init for details).
 set_parameters_from_list(parameterslist)
Sets the parameters of the model from a list
Parameters
 parametersaslistlist
The new parameter values as a list, where the first len(self.hyperparameters) values are the parameter values for the first outcome (the first element of self.outcomes), the second set of len(self.hyperparameters) values are for the second outcome in this list, and so on, up to the second last value of self.outcomes.
Returns
None
 parameters_as_list()
Returns the parameters as a list, in the same format as when input to set_parameters_from_list. See the docstring of that method for more info.
 parameters_copy()
Returns the values of the parameters, in the dictionary form in which it is internally stored.
 probabilities(times, trim=True)
Returns the probability distribution for each time in times.
Parameters
 timeslist
A list of times, to return the probability distributions for.
 timebool, optional
Whether or not to set probability > 1 to 1 and probabilities < 0 to 0. If set to True then there is no guarantee that the probabilities will sum to 1 at all times anymore.
Returns
 dict
A dictionary where the keys are the possible outcomes, and the value for a key is a list (of the same lengths as times) containing the probability for that outcome at the times in times.
 class pygsti.extras.drift.probtrajectory.ConstantProbTrajectory(outcomes, probabilities)
Bases:
ProbTrajectory
Encapulates a timedependent probability distribution that is actually a constant. Useful when wanting to encode a constant probability distribution in a way that can be used consistently with any other ProbTrajectory object.
Initializes a ConstantProbTrajectory object.
Parameters
 outcomeslist
What the probability distribution is over. Typically, all possible outcomes for the circuit that this is a probability trajectory for.
 probabilitiesdict
The static probability to obtained all but the last outcome (which is set by the other probabilities).
Returns
A new ConstantProbTrajectory object.
 basisfunction(i, times)
 class pygsti.extras.drift.probtrajectory.CosineProbTrajectory(outcomes, hyperparameters, parameters, starttime, timestep, numtimes)
Bases:
ProbTrajectory
Encapulates a timedependent probability distribution that is parameterized as a sum of cosines. Specifically, it is parameterized as the sum of the TypeII DCT basis functions.
Initializes a CosineProbTrajectory object.
Parameters
 outcomeslist
What the probability distribution is over. Typically, all possible outcomes for the circuit that this is a probability trajectory for.
 hyperparameterslist
A set of integers, that specify the indices of the the DCT basis functions to include. This must include 0 as the first element, corresponding to the constant component of the probability trajectories.
 parametersdict
A dictonary where the keys are all but the last element of outcomes, and the elements are lists of the same lengths as hyperparameters. These are amplitudes for the DCT basis functions, for each outcome. The first element of each list is the constant component of the that probability trajectory.
 starttimefloat
The start time of the time period over which the DCT basis functions are being defined. This is typically set to the first data collection time of the circuit that this probability trajectory is being defined for.
 timestepfloat
The size of the time step used to define the DCT basis functions. This is typically set to the time step between the data collection times of the circuit that this probability trajectory is being defined for
 numtimesint
The number of data collection times defining the DCT basis functions (defines the total number of DCT basis functions: the hyperparameters list is then a subset of this [0,1,2,…,numtimes1]). This is typically set to the number of data collection times for the circuit that this probability trajectory is being defined for.
Returns
A new CosineProbTrajectory object.
 basisfunction(i, times)
The ith TypeII DCT basis function, evaluated at the specified times, where the DCT basis functions under consideration are defined by the time parameters set in the initialization.
The normalization of the functions is such that the max/min of each function is +1/1.
Parameters
 iint
The frequency index of the DCT basis function.
 timeslist
The times to evaluate the basis function at
Returns
 array
The value of the basis function at the specified times.
 pygsti.extras.drift.probtrajectory.negloglikelihood(probtrajectory, clickstreams, times, minp=0.0, maxp=1.0)
The negative loglikelihood of a ProbTrajectory, modelling a timedependent probability distribution.
Parameters
 modelProbTrajectory
The model to find the loglikelihood of.
 datadict
The data, consisting of a counts timeseries for each measurement outcome. This is a dictionary whereby the keys are the outcome labels and the values are list (or arrays) giving the number of times that measurement outcome was observed at the corresponding time in the times list.
 timeslist or array
The times associated with the data. The probabilities are extracted from the model at these times, using the model.get_probabilites method .
 minpfloat, optional
A positive value close to zero. The value of p below which x*log(p) is approximated using a Taylor expansion (used to smooth out the parameter boundaries and obtain better fitting performance). The default value of 0. give the true loglikelihood.
 maxpfloat, optional
A positive value close to and <= 1. The value of p above which x*log(p) the boundary on p being <= 1 is enforced using a smooth, quickly growing function. If set to 1. it gives the true loglikelihood.
Returns
 float
The loglikehood of the model given the timeseries data.
 pygsti.extras.drift.probtrajectory.probsdict_negloglikelihood(probs, clickstreams, minp=0.0, maxp=1.0)
The negative loglikelihood of varying probabilities probs, evaluated for the data streams in clickstreams.
Parameters
 probsdict
A dictionary where the keys are the outcome strings in the clickstream (its keys) and the value for an outcome is the timedependent probability list for that outcome, at the times associated with the data in the clickstreams.
 clickstreamsdict
A dictionary where the keys are the different measurement outcomes, and the values are lists that give counts for that measurement outcome.
Returns
 float
The negative logilikelihood of the probability trajectories given the clickstream data.
 pygsti.extras.drift.probtrajectory.maxlikelihood(probtrajectory, clickstreams, times, minp=0.0001, maxp=0.999999, method='NelderMead', return_opt_output=False, options=None, verbosity=1)
Implements maximum likelihood estimation over a model for a timeresolved probabilities trajectory, and returns the maximum likelihood model.
Parameters
 modelProbTrajectory
The model for which to maximize the likelihood of the parameters. The value of the parameters in the input model is used as the seed.
 clickstreamsdict
The data, consisting of a counts timeseries for each measurement outcome. This is a dictionary whereby the keys are the outcome labels and the values are list (or arrays) giving the number of times that measurement outcome was observed at the corresponding time in the times list.
 timeslist or array
The times associated with the data. The probabilities are extracted from the model at these times (see the model.get_probabilites method), to implement the model parameters optimization.
 minpfloat, optional
A positive value close to zero. The value of p below which x*log(p) is approximated using a Taylor expansion (used to smooth out the parameter boundaries and obtain better fitting performance). The default value should be fine.
 maxpfloat, optional
A positive value close to and <= 1. The value of p above which x*log(p) the boundary on p being <= 1 is enforced using a smooth, quickly growing function. The default value should be fine.
 methodstr, optional
Any value allowed for the method parameter in scipy.optimize.minimize().
 verbosityint, optional
The amount of print to screen.
 return_opt_outputbool, optional
Whether or not to return the output of the optimizer.
Returns
 ProbTrajectory
The maximum likelihood model returned by the optimizer.
 if return_opt_output:
 optout
The output of the optimizer.
 pygsti.extras.drift.probtrajectory.amplitude_compression(probtrajectory, times, epsilon=0.0, verbosity=1)
Reduces the amplitudes in a CosineProbTrajectory model until the model is valid, i.e., all probabilities are within [0, 1]. Also rectifies any of the constant components of the probability trajectories that are slightly outside [0, 1].
Parameters
 probtrajectory: CosineProbTrajectory
The model on which to perform the amplitude reduction
 times: list
The times at which to enforce the validity of the model (this algorithm does not guarantee that the probabilities will be within [0, 1] at all times in the reals).
 epsilon: float, optional
The amplitudes are compressed so that all the probabilities are within [0+epsilon,1epsilon] at all times. Setting this to be larger than 0 can be useful as it guarantees that the resultant probability trajectory has a nonzero likelihood.
Returns
 CosineProbTrajectory
The new model, that may have had the amplitudes reduced
 Bool
Whether or not the function did anything nontrivial, i.e, whether any compression was required.