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.

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’	$X(\phi) Y(\theta) X(\lambda)$	$e^{i\gamma} R_X(\phi).R_Y(\theta).R_X(\lambda)$
‘U3’	$Z(\phi) Y(\theta) Z(\lambda)$	$e^{i\gamma} U_3(\theta,\phi,\lambda)$
‘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’	$Z(\phi) Y(\theta) Z(\lambda)$	$e^{i\gamma} U_1(\phi+\pi).R_X\left(\frac{\pi}{2}\right).$ $R_Z(\theta+\pi).S_X\left(\frac{\pi}{2}\right).U_1(\lambda)$
‘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’, ‘ZSX’, ‘U3’, ‘U1X’, ‘RR’, ‘ZYZ’, ‘ZXZ’, ‘XYX’.

Parameters

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

Raises

QiskitError – If input basis is not recognized.

init

__init__(basis='U3')

Initialize decomposer

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

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

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

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

basis

The decomposition basis.

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