OneQubitEulerDecomposer

qiskit.synthesis.OneQubitEulerDecomposer(basis='U3', use_dag=False)

Bases: object(opens in a new tab)

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’	$X(\phi) Y(\theta) X(\lambda)$	$e^{i\gamma} R_X(\phi).R_Y(\theta).R_X(\lambda)$
‘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’	$Z(\phi) Y(\theta) Z(\lambda)$	$e^{i\gamma} R\left(-\pi,\frac{\phi-\lambda+\pi}{2}\right).$ $R\left(\theta+\pi,\frac{\pi}{2}-\lambda\right)$

call

__call__(unitary, simplify=True, atol=1e-12)

GitHub

Decompose single qubit gate into a circuit.

Parameters

unitary (Operator |Gate | np.ndarray) – 1-qubit unitary matrix
simplify (bool(opens in a new tab)) – reduce gate count in decomposition [Default: True].
atol (float(opens in a new tab)) – absolute tolerance for checking angles when simplifying returned circuit [Default: 1e-12].

Returns

the decomposed single-qubit gate circuit

Return type

QuantumCircuit

Raises

QiskitError – if input is invalid or synthesis fails.

Initialize decomposer

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

Parameters

basis (str(opens in a new tab)) – the decomposition basis [Default: 'U3']
use_dag (bool(opens in a new tab)) – If true the output from calls to the decomposer will be a DAGCircuit object instead of QuantumCircuit.