qiskit.quantum_info.OneQubitEulerDecomposer

class OneQubitEulerDecomposer(basis='U3')

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.

__init__(basis='U3')

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

__init__([basis])	Initialize decomposer
angles(unitary)	Return the Euler angles for input array.
angles_and_phase(unitary)	Return the Euler angles and phase for input array.

Attributes

basis

The decomposition basis.

angles(unitary)

Return the Euler angles for input array.

Parameters

unitary (np.ndarray) – 2x2 unitary matrix.

Returns

(theta, phi, lambda).

Return type

tuple

angles_and_phase(unitary)

Return the Euler angles and phase for input array.

Parameters

unitary (np.ndarray) – 2x2 unitary matrix.

Returns

(theta, phi, lambda, phase).

Return type

tuple

property basis

The decomposition basis.