Skip to main contentIBM Quantum Documentation
This page is from an old version of Qiskit SDK and does not exist in the latest version. We recommend you migrate to the latest version. See the release notes for more information.

OneQubitEulerDecomposer

class OneQubitEulerDecomposer(basis='U3', use_dag=False)

GitHub

Bases: object

A class for decomposing 1-qubit unitaries into Euler angle rotations.

The resulting decomposition is parameterized by 3 Euler rotation angle parameters (θ,ϕ,λ)(\theta, \phi, \lambda), and a phase parameter γ\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(ϕ)Y(θ)Z(λ)Z(\phi) Y(\theta) Z(\lambda)eiγRZ(ϕ).RY(θ).RZ(λ)e^{i\gamma} R_Z(\phi).R_Y(\theta).R_Z(\lambda)
‘ZXZ’Z(ϕ)X(θ)Z(λ)Z(\phi) X(\theta) Z(\lambda)eiγRZ(ϕ).RX(θ).RZ(λ)e^{i\gamma} R_Z(\phi).R_X(\theta).R_Z(\lambda)
‘XYX’X(ϕ)Y(θ)X(λ)X(\phi) Y(\theta) X(\lambda)eiγRX(ϕ).RY(θ).RX(λ)e^{i\gamma} R_X(\phi).R_Y(\theta).R_X(\lambda)
‘XZX’X(ϕ)Z(θ)X(λ)X(\phi) Z(\theta) X(\lambda)eiγRX(ϕ).RZ(θ).RX(λ)e^{i\gamma} R_X(\phi).R_Z(\theta).R_X(\lambda)
‘U3’Z(ϕ)Y(θ)Z(λ)Z(\phi) Y(\theta) Z(\lambda)eiγU3(θ,ϕ,λ)e^{i\gamma} U_3(\theta,\phi,\lambda)
‘U321’Z(ϕ)Y(θ)Z(λ)Z(\phi) Y(\theta) Z(\lambda)eiγU3(θ,ϕ,λ)e^{i\gamma} U_3(\theta,\phi,\lambda)
‘U’Z(ϕ)Y(θ)Z(λ)Z(\phi) Y(\theta) Z(\lambda)eiγU3(θ,ϕ,λ)e^{i\gamma} U_3(\theta,\phi,\lambda)
‘PSX’Z(ϕ)Y(θ)Z(λ)Z(\phi) Y(\theta) Z(\lambda)eiγU1(ϕ+π).RX(π2).e^{i\gamma} U_1(\phi+\pi).R_X\left(\frac{\pi}{2}\right). U1(θ+π).RX(π2).U1(λ)U_1(\theta+\pi).R_X\left(\frac{\pi}{2}\right).U_1(\lambda)
‘ZSX’Z(ϕ)Y(θ)Z(λ)Z(\phi) Y(\theta) Z(\lambda)eiγRZ(ϕ+π).X.e^{i\gamma} R_Z(\phi+\pi).\sqrt{X}. RZ(θ+π).X.RZ(λ)R_Z(\theta+\pi).\sqrt{X}.R_Z(\lambda)
‘ZSXX’Z(ϕ)Y(θ)Z(λ)Z(\phi) Y(\theta) Z(\lambda)eiγRZ(ϕ+π).X.RZ(θ+π).X.RZ(λ)e^{i\gamma} R_Z(\phi+\pi).\sqrt{X}.R_Z(\theta+\pi).\sqrt{X}.R_Z(\lambda) or eiγRZ(ϕ+π).X.RZ(λ)e^{i\gamma} R_Z(\phi+\pi).X.R_Z(\lambda)
‘U1X’Z(ϕ)Y(θ)Z(λ)Z(\phi) Y(\theta) Z(\lambda)eiγU1(ϕ+π).RX(π2).e^{i\gamma} U_1(\phi+\pi).R_X\left(\frac{\pi}{2}\right). U1(θ+π).RX(π2).U1(λ)U_1(\theta+\pi).R_X\left(\frac{\pi}{2}\right).U_1(\lambda)
‘RR’Z(ϕ)Y(θ)Z(λ)Z(\phi) Y(\theta) Z(\lambda)eiγR(−π,ϕ−λ+π2).e^{i\gamma} R\left(-\pi,\frac{\phi-\lambda+\pi}{2}\right). R(θ+π,π2−λ)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

  • 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.

Raises

QiskitError – If input basis is not recognized.

Methods

angles

OneQubitEulerDecomposer.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

OneQubitEulerDecomposer.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

build_circuit

OneQubitEulerDecomposer.build_circuit(gates, global_phase)

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

Attributes

basis

The decomposition basis.

Was this page helpful?
Report a bug or request content on GitHub.