# OneQubitEulerDecomposer

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

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.

BasisEuler Angle BasisDecomposition 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

Raises

QiskitError – If input basis is not recognized.

## Attributes

### basis

The decomposition basis.

## Methods

### angles

angles(unitary)

Return the Euler angles for input array.

Parameters

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

Returns

(theta, phi, lambda).

Return type

tuple (opens in a new tab)

### 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 (opens in a new tab)

### build_circuit

build_circuit(gates, global_phase)

Return the circuit or dag object from a list of gates.