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# OneQubitEulerDecomposer¶

class OneQubitEulerDecomposer(basis='U3', use_dag=False)[source]

Bases : object

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 14 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”.

Paramètres
• basis (str) – the decomposition basis [Default: “U3”]

• use_dag (bool) – If true the output from calls to the decomposer will be a DAGCircuit object instead of QuantumCircuit.

Lève

QiskitError – If input basis is not recognized.

Methods

 angles Return the Euler angles for input array. angles_and_phase Return the Euler angles and phase for input array. build_circuit Return the circuit or dag object from a list of gates.

Attributes

basis

The decomposition basis.