I'm trying to test Clifford gates in qiskit according to the table in Fault-tolerant SQ, page 101. I tried 4 Cliffords in the test $$-X/2 - X -X/2,Y/2,X/2 - -X/2,Y/2,-X/2$$
using the following code
import numpy as np
from qiskit import QuantumCircuit, Aer, execute
from qiskit.quantum_info import Operator
qc = QuantumCircuit(1)
qc.rx(-np.pi/2, 0)
qc.rx(np.pi, 0)
qc.rx(-np.pi/2, 0)
qc.ry(np.pi/2, 0)
qc.rx(np.pi/2, 0)
# 4th
qc.rx(-np.pi/2, 0)
qc.ry(np.pi/2, 0)
qc.rx(-np.pi/2, 0)
print('Final matrix:', Operator(qc).data)
qc.draw('mpl')
which gives me the output:
Final matrix: [[ 0. +0.707j -0.707+0.j ]
[ 0.707+0.j 0. -0.707j]]
next, I found the inverse of this:
np.linalg.inv(Operator(qc).data)
which gives me:
[[ 0. -0.707j 0.707+0.j ]
[-0.707+0.j -0. +0.707j]]
and didn't find the corresponding Clifford in the table as I was expeccting.
What do I do wrong in my calculations in qiskit?