mimiqcircuits.operations.gates.standard.deprecated

Deprecated gates (U1, U2, U3).

Classes

GateU1(lmbda)	Single qubit generic unitary gate \({U_1}\).
GateU2(phi, lmbda)	Single qubit generic unitary gate \({U_2}\).
GateU3(theta, phi, lmbda)	Single qubit generic unitary gate \({U_3}\).

class mimiqcircuits.operations.gates.standard.deprecated.GateU1(lmbda)

Bases: Gate

Single qubit generic unitary gate \({U_1}\).

Equivalent to GateP()

Matrix representation:

\[\begin{split}\operatorname{U1}(\lambda) = \begin{pmatrix} 1 & 0 \\ 0 & e^{i\lambda} \end{pmatrix}\end{split}\]

Parameters:

lambda (float) – Euler angle 3 in radians.

Examples

>>> from mimiqcircuits import *
>>> from symengine import *
>>> lmbda = Symbol('lambda')
>>> GateU1(lmbda)
U1(lambda)
>>> GateU1(lmbda).matrix()
[1.0, 0]
[0, exp(I*lambda)]

>>> c = Circuit().push(GateU1(lmbda), 0)
>>> c
1-qubit circuit with 1 instruction:
└── U1(lambda) @ q[0]

>>> GateU1(lmbda).power(2), GateU1(lmbda).inverse()
(U1(2*lambda), U1(-lambda))
>>> GateU1(lmbda).decompose()
1-qubit circuit with 1 instruction:
└── U(0, 0, lambda, 0.0) @ q[0]

__init__(lmbda)

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.

class mimiqcircuits.operations.gates.standard.deprecated.GateU2(phi, lmbda)

Bases: Gate

Single qubit generic unitary gate \({U_2}\).

Matrix representation:

\[\begin{split}\operatorname{U2}(\phi,\lambda) = \frac{1}{\sqrt{2}}e^{-(\phi+\lambda)/2}\begin{pmatrix} 1 & -e^{i\lambda} \\ e^{i\phi} & e^{i(\phi+\lambda)} \end{pmatrix}\end{split}\]

Parameters:

• phi – Euler angle in radians.

• lambda – Euler angle in radians.

Examples

>>> from mimiqcircuits import *
>>> from symengine import *
>>> phi, lmbda = symbols('phi lambda')
>>> GateU2(phi, lmbda)
U2(phi, lambda)
>>> GateU2(phi, lmbda).matrix()
[0.707106781186548, -0.707106781186548*exp(I*lambda)]
[0.707106781186548*exp(I*phi), 0.707106781186548*exp(I*(lambda + phi))]

>>> c = Circuit().push(GateU2(phi, lmbda), 0)
>>> c
1-qubit circuit with 1 instruction:
└── U2(phi, lambda) @ q[0]

>>> GateU2(phi, lmbda).power(2), GateU2(phi, lmbda).inverse()
(U2(phi, lambda)**2, U2(-lambda - pi, -phi + pi))
>>> GateU2(phi, lmbda).decompose()
1-qubit circuit with 1 instruction:
└── U((1/2)*pi, phi, lambda, 0.0) @ q[0]

__init__(phi, lmbda)

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.

class mimiqcircuits.operations.gates.standard.deprecated.GateU3(theta, phi, lmbda)

Bases: Gate

Single qubit generic unitary gate \({U_3}\).

This gate is equivalent to GateU() up to a global phase, \(\operatorname{U3}(\theta,\phi,\lambda) = e^{-i(\phi + \lambda + \theta)/2} \operatorname{U}(\theta,\phi,\lambda)\)

Matrix representation:

\[\begin{split}\operatorname{U3}(\theta,\phi,\lambda) = \frac{1}{2}e^{-i(\phi + \lambda + \theta)/2} \begin{pmatrix} 1 + e^{i\theta} & -i e^{i\lambda}(1 - e^{i\theta}) \\ i e^{i\phi}(1 - e^{i\theta}) & e^{i(\phi + \lambda)}(1 + e^{i\theta}) \end{pmatrix}\end{split}\]

Parameters:

• theta – Euler angle 1 in radians.

• phi – Euler angle 2 in radians.

• lambda – Euler angle 3 in radians.

Examples

>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta, phi, lmbda = symbols('theta phi lambda')
>>> GateU3(theta, phi, lmbda)
U3(theta, phi, lambda)
>>> GateU3(theta, phi, lmbda).matrix()
[1.0*cos((1/2)*theta), -exp(I*lambda)*sin((1/2)*theta)]
[exp(I*phi)*sin((1/2)*theta), exp(I*(lambda + phi))*cos((1/2)*theta)]

>>> c = Circuit().push(GateU3(theta, phi, lmbda), 0)
>>> GateU3(theta, phi, lmbda).power(2), GateU3(theta, phi, lmbda).inverse()
(U3(theta, phi, lambda)**2, U3(-theta, -lambda, -phi))
>>> GateU3(theta, phi, lmbda).decompose()
1-qubit circuit with 1 instruction:
└── U(theta, phi, lambda, 0.0) @ q[0]

__init__(theta, phi, lmbda)

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.