Note

This is the documentation for the current state of the development branch of Qiskit Experiments. The documentation or APIs here can change prior to being released.

Probability

class Probability(outcome, alpha_prior=0.5, validate=True)

Compute the mean probability of a single measurement outcome from counts.

This node returns the mean and standard deviation of a single measurement outcome probability \(p\) estimated from the observed counts. The mean and variance are computed from the posterior Beta distribution \(B(\alpha_0^\prime,\alpha_1^\prime)\) estimated from a Bayesian update of a prior Beta distribution \(B(\alpha_0, \alpha_1)\) given the observed counts.

The mean and variance of the Beta distribution \(B(\alpha_0, \alpha_1)\) are:

\[\text{E}[p] = \frac{\alpha_0}{\alpha_0 + \alpha_1}, \quad \text{Var}[p] = \frac{\text{E}[p] (1 - \text{E}[p])}{\alpha_0 + \alpha_1 + 1}\]

Given a prior Beta distribution \(B(\alpha_0, \alpha_1)\), the posterior distribution for the observation of \(F\) counts of a given outcome out of \(N\) total shots is a \(B(\alpha_0^\prime,\alpha_1^\prime):math:\) with

\[\alpha_0^\prime = \alpha_0 + F, \quad \alpha_1^\prime = \alpha_1 + N - F.\]

Note

The default value for the prior distribution is Jeffery’s Prior \(\alpha_0 = \alpha_1 = 0.5\) which represents ignorance about the true probability value. Note that for this prior the mean probability estimate from a finite number of counts can never be exactly 0 or 1. The estimated mean and variance are given by

\[\text{E}[p] = \frac{F + 0.5}{N + 1}, \quad \text{Var}[p] = \frac{\text{E}[p] (1 - \text{E}[p])}{N + 2}\]

This node will deprecate standard error provided by the previous node.

Initialize a counts to probability data conversion.

Parameters:

• outcome (str) – The bitstring for which to return the probability and variance.

• alpha_prior (float | Sequence[float]) – A prior Beta distribution parameter [alpha0, alpha1]. If specified as float this will use the same value for alpha0 and alpha1 (Default: 0.5).

• validate (bool) – If set to False the DataAction will not validate its input.

Raises:

DataProcessorError – When the dimension of the prior and expected parameter vector do not match.

Methods

__call__(data)

Call the data action of this node on the data.

Parameters:

data (ndarray) – A numpy array with arbitrary dtype. If the elements are ufloat objects consisting of a nominal value and a standard error, then the error propagation is done automatically.

Returns:

The processed data.

Return type:

ndarray