Part a:
Gate
H
X
Y
Z
S
T
R_x
R_y
Theta
pi
pi
pi
pi
pi/2
pi/4
pi/2
pi/2
n_alpha
(1/sqrt(2))*(1,0,1)
(1,0,0)
(0,1,0)
(0,0,1)
(0,0,1)
(0,0,1)
(1,0,0)
(0,1,0)
Using the info from the table and equation 1, I find:
U_H=(i/sqrt(2))*[1,1;1,-1]
U_X=i*[0,1;1,0]
U_Y=i*[0,-i;i,0]
U_Z=i*[1,0;0,-1]...