Unnecessary warning of non-trace-1 argument to psd_square_root in fidelity function

[rileyjmurray]

The fidelity function contains a helper function called psd_square_root, which currently raises a warning if the input argument isn't trace-1:

pyGSTi/pygsti/tools/optools.py

Lines 157 to 178 in c3f1f84

	def psd_square_root(mat):
	evals, U = _np.linalg.eigh(mat)
	if _np.min(evals) < -__SCALAR_TOL__:
	message = f"""
	Input matrix is not PSD up to tolerance {__SCALAR_TOL__}.
	We'll project out the bad eigenspaces to only work with the PSD part.
	"""
	_warnings.warn(message)
	evals[evals < 0] = 0.0
	tr = _np.sum(evals)
	if abs(tr - 1) > __VECTOR_TOL__:
	message = f"""
	The PSD part of the input matrix is not trace-1 up to tolerance {__VECTOR_TOL__}.
	Beware result!
	"""
	_warnings.warn(message)
	sqrt_mat = U @ (_np.sqrt(evals).reshape((-1, 1)) * U.T.conj())
	return sqrt_mat
	sqrt_a = psd_square_root(a)
	tr_arg = psd_square_root(sqrt_a @ b @ sqrt_a)
	f = _np.trace(tr_arg).real ** 2 # Tr( sqrt{ sqrt(a) * b * sqrt(a) } )^2

This function is called twice, immediately after its definition. But the trace check should only really be applied the first time that psd_square_root is called. Warnings raised in the second call are entirely unnecessary.

An obvious fix is to remove this check from psd_square_root and just check if the first input argument is trace-1 before calling psd_square_root. The reason for including the trace check inside psd_square_root was because we compute the trace after projecting out negative eigenspaces.

This is an easy fix for me but I'm in the middle of other work so I'm leaving a note to fix later.

[rileyjmurray]

Resolved by #622. Waiting to close until we make a pypi release with this fix.

[coreyostrove]

Fix now live on pypi, closing.