# OneQubitEulerDecomposer¶

class OneQubitEulerDecomposer(basis='U3')[source]

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 17 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’

$$X(\phi) Y(\theta) X(\lambda)$$

$$e^{i\gamma} R_X(\phi).R_Y(\theta).R_X(\lambda)$$

‘U3’

$$Z(\phi) Y(\theta) Z(\lambda)$$

$$e^{i\gamma}{2}\right)\right)} U_3(\theta,\phi,\lambda)$$

‘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: ‘U3’, ‘U1X’, ‘RR’, ‘ZYZ’, ‘ZXZ’, ‘XYX’.

Parameters

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

Raises

QiskitError – If input basis is not recognized.

Attributes

 OneQubitEulerDecomposer.basis The decomposition basis.

Methods

 OneQubitEulerDecomposer.__call__(unitary[, …]) Decompose single qubit gate into a circuit. Return the Euler angles for input array. Return the Euler angles and phase for input array.