Remove usage of np.polyfit

[purva-thakre]

We use numpy.polyfit to define the extrapolation methods for ZNE. The related API in numpy has since changed to using numpy.polynomial instead of numpy.polyfit.

mitiq/mitiq/zne/inference.py

Lines 155 to 158 in 9e1cbb5

	) -> Tuple[List[float], Optional[npt.NDArray[np.float64]]]:
	"""Fits the ansatz to the (scale factor, expectation value) data using
	``numpy.polyfit``, returning the optimal parameters and covariance matrix
	of the parameters.

The transition guide has a helpful table for adjusting to the newer changes.

https://numpy.org/doc/stable/reference/generated/numpy.polynomial.polynomial.polyfit.html

[purva-thakre]

Looked into what this entails. With the newer API, the covariance matrix option was removed in np.polynomial.polynomial.polyfit.

Tests will fail due to TypeError: polyfit() got an unexpected keyword argument 'cov'.

mitiq/mitiq/zne/inference.py

Line 179 in b58f029

scale_factors, exp_values, deg, w=weights, cov=True

So, we will have to work around numpy/numpy#20871 or keep using the older API.

There are two open PRs to allow the covariance matrix option in np.polynomial.polynomial.polyfit as a cov kwarg or a fit_with_covariance function. One has an inactive label. It's difficult to tell if cov will be an available option in the newer API.

[cosenal]

It looks like the covariance matrix is used to calculate the error of the fit in

mitiq/mitiq/zne/inference.py

Line 864 in 4c66456

zne_error = np.sqrt(params_cov[order, order])

If one passes full=True to np.polynomial.polynomial.polyfit, they can then get the residuals of the fit and perhaps calculate the error from there?

[purva-thakre]

they can then get the residuals of the fit and perhaps calculate the error from there?

By defining a function for this in mitiq, right?