mimiqcircuits.operations.gates.standard.u

U (Generic Unitary) gate.

Classes

GateU(theta, phi, lmbda[, gamma])

Single qubit generic unitary phase gate.

class mimiqcircuits.operations.gates.standard.u.GateU(theta, phi, lmbda, gamma=0.0)

Bases: Gate

Single qubit generic unitary phase gate.

Matrix representation:

\[\begin{split}\operatorname{U}(\theta, \phi, \lambda, \gamma) = \mathrm{e}^{i\gamma} \begin{pmatrix} \cos\left(\frac{\theta}{2}\right) & -\mathrm{e}^{i\lambda}\sin\left(\frac{\theta}{2}\right)\\ \mathrm{e}^{i\phi}\sin\left(\frac{\theta}{2}\right) & \mathrm{e}^{i(\phi+\lambda)}\cos\left (\frac{\theta}{2}\right) \end{pmatrix}\end{split}\]

Parameters:

• theta (float) – Euler angle 1 in radians.

• phi (float) – Euler angle 2 in radians.

• lambda (float) – Euler angle 3 in radians.

• gamma (float, optional) – Euler angle 4 in radians (default is 0).

Examples

>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta, phi, lmbda, gamma = symbols('theta phi lambda gamma')
>>> GateU(theta, phi, lmbda, gamma)
U(theta, phi, lambda, gamma)
>>> GateU(theta, phi, lmbda, gamma).matrix()
[exp(I*gamma)*cos((1/2)*theta), -exp(I*(gamma + lambda))*sin((1/2)*theta)]
[exp(I*(gamma + phi))*sin((1/2)*theta), exp(I*(gamma + lambda + phi))*cos((1/2)*theta)]

>>> c = Circuit().push(GateU(theta, phi, lmbda, gamma), 0)
>>> c
1-qubit circuit with 1 instruction:
└── U(theta, phi, lambda, gamma) @ q[0]

>>> GateU(theta, phi, lmbda, gamma).power(2), GateU(theta, phi, lmbda, gamma).inverse()
(U(theta, phi, lambda, gamma)**2, U(-theta, -lambda, -phi, -gamma))
>>> GateU(theta, phi, lmbda, gamma).decompose()
1-qubit circuit with 1 instruction:
└── U(theta, phi, lambda, gamma) @ q[0]

>>> c = Circuit().push(GateU(theta, phi, lmbda, gamma), 0)
>>> c
1-qubit circuit with 1 instruction:
└── U(theta, phi, lambda, gamma) @ q[0]

>>> GateU(theta, phi, lmbda, gamma).power(2), GateU(theta, phi, lmbda, gamma).inverse()
(U(theta, phi, lambda, gamma)**2, U(-theta, -lambda, -phi, -gamma))
>>> GateU(theta, phi, lmbda, gamma).decompose()
1-qubit circuit with 1 instruction:
└── U(theta, phi, lambda, gamma) @ q[0]

__init__(theta, phi, lmbda, gamma=0.0)

inverse()

Raise an error, as non-unitary operators cannot be inverted.

This method is not implemented for non-unitary operators and will raise a NotImplementedError if called.

Raises:

NotImplementedError – If the method is called.

convert_to_numeric(matrix)

Convert a symbolic matrix to a numeric numpy array.