I have this 2*2 unitary matrix one looks like U =[ -0.2840 - 0.5319i, -0.0000 - 0.7978i; -0.0000 - 0.7978i ,-0.2840 + 0.5319i] I want to represent this unitary matrix by a CU3 gate which looks like
Can someone suggest a faster way to determine all the angles? Is there any open-source code that I can use to determine these angles? Thank you for any help and suggestions.
You can essentially just read off those angles. Consider the top-left matrix element $$ U_{00}=-0.2840-0.5319i=e^{i\gamma}\cos(\theta/2). $$ If you take the mod-square, you get $$ |U_{00}|^2=0.2840^2+0.5319^2=\cos^2(\theta/2). $$ From there, $$ e^{i\gamma}=U_{00}/\cos(\theta/2). $$ Alternatively, $$ \tan\gamma=\frac{-0.5319}{-0.2840}. $$
You can use Qiskit's OneQubitEulerDecomposer class as follows:
from qiskit.quantum_info.synthesis.one_qubit_decompose import OneQubitEulerDecomposer
import numpy as np
unitary = np.array([
[-0.284 - 0.5319j, -0.0 - 0.7978j],
[ -0.0 - 0.7978j ,-0.284 + 0.5319j]
])
decomposer = OneQubitEulerDecomposer('U3')
theta, phi, lambda_, gamma = decomposer.angles_and_phase(unitary)
