OneQubitEulerDecomposer

class OneQubitEulerDecomposer(basis='U3')

Bases: object

A class for decomposing 1-qubit unitaries into Euler angle rotations.

The resulting decomposition is parameterized by 3 Euler rotation angle parameters \((\theta, \phi, \lambda)\), and a phase parameter \(\gamma\). The value of the parameters for an input unitary depends on the decomposition basis. Allowed bases and the resulting circuits are shown in the following table. Note that for the non-Euler bases (U3, U1X, RR), the ZYZ Euler parameters are used.

Table 19 Supported circuit bases

Basis	Euler Angle Basis	Decomposition Circuit
‘ZYZ’	\(Z(\phi) Y(\theta) Z(\lambda)\)	\(e^{i\gamma} R_Z(\phi).R_Y(\theta).R_Z(\lambda)\)
‘ZXZ’	\(Z(\phi) X(\theta) Z(\lambda)\)	\(e^{i\gamma} R_Z(\phi).R_X(\theta).R_Z(\lambda)\)
‘XYX’	\(X(\phi) Y(\theta) X(\lambda)\)	\(e^{i\gamma} R_X(\phi).R_Y(\theta).R_X(\lambda)\)
‘XZX’	\(X(\phi) Z(\theta) X(\lambda)\)	\(e^{i\gamma} R_X(\phi).R_Z(\theta).R_X(\lambda)\)
‘U3’	\(Z(\phi) Y(\theta) Z(\lambda)\)	\(e^{i\gamma} U_3(\theta,\phi,\lambda)\)
‘U321’	\(Z(\phi) Y(\theta) Z(\lambda)\)	\(e^{i\gamma} U_3(\theta,\phi,\lambda)\)
‘U’	\(Z(\phi) Y(\theta) Z(\lambda)\)	\(e^{i\gamma} U_3(\theta,\phi,\lambda)\)
‘PSX’	\(Z(\phi) Y(\theta) Z(\lambda)\)	\(e^{i\gamma} U_1(\phi+\pi).R_X\left(\frac{\pi}{2}\right).\) \(U_1(\theta+\pi).R_X\left(\frac{\pi}{2}\right).U_1(\lambda)\)
‘ZSX’	\(Z(\phi) Y(\theta) Z(\lambda)\)	\(e^{i\gamma} R_Z(\phi+\pi).\sqrt{X}.\) \(R_Z(\theta+\pi).\sqrt{X}.R_Z(\lambda)\)
‘ZSXX’	\(Z(\phi) Y(\theta) Z(\lambda)\)	\(e^{i\gamma} R_Z(\phi+\pi).\sqrt{X}.R_Z(\theta+\pi).\sqrt{X}.R_Z(\lambda)\) or \(e^{i\gamma} R_Z(\phi+\pi).X.R_Z(\lambda)\)
‘U1X’	\(Z(\phi) Y(\theta) Z(\lambda)\)	\(e^{i\gamma} U_1(\phi+\pi).R_X\left(\frac{\pi}{2}\right).\) \(U_1(\theta+\pi).R_X\left(\frac{\pi}{2}\right).U_1(\lambda)\)
‘RR’	\(Z(\phi) Y(\theta) Z(\lambda)\)	\(e^{i\gamma} R\left(-\pi,\frac{\phi-\lambda+\pi}{2}\right).\) \(R\left(\theta+\pi,\frac{\pi}{2}-\lambda\right)\)

Initialize decomposer

Supported bases are: ‘U’, ‘PSX’, ‘ZSXX’, ‘ZSX’, ‘U321’, ‘U3’, ‘U1X’, ‘RR’, ‘ZYZ’, ‘ZXZ’, ‘XYX’, ‘XZX’.

Parameters

basis (str) – the decomposition basis [Default: ‘U3’]

Raises

QiskitError – If input basis is not recognized.

Methods

angles	Return the Euler angles for input array.
angles_and_phase	Return the Euler angles and phase for input array.

Attributes

basis

The decomposition basis.