extra CNOT inserted in Patel-Hayes-Markov algorithm

[ajavadia]

#2457 added the graysynth and patel-hayes-markov synthesis algorithms.

However the doubly-controlled Z rotation synthesis from Figure 3 of the associated paper seems not to be synthesized accurately.

A 6-cnot construction should be found according to the paper:

but currently qiskit finds a 7-cnot construction:

Code for the above:

from qiskit.transpiler.synthesis import graysynth
cnots = [[1, 0, 1, 0, 1, 1, 0],
         [0, 1, 0, 1, 1, 1, 0],
         [0, 0, 1, 1, 1, 0, 1]]
angles = [1/8, 1/8, 3/8, 3/8, 1/8, 3/8, 1/8]
c_gray = graysynth(cnots, angles, 3)
c_gray.draw(output='mpl')