mimiqcircuits.operations.gates.standard.rotations

Rotation gates (RX, RY, RZ, R).

Classes

GateR(theta, phi)	Single qubit Rotation gate around the axis \(\cos(\phi)\hat{x} + \sin(\phi)\hat{y}\).
GateRX(theta)	Single qubit Rotation gate around the axis \(\hat{x}\)
GateRY(theta)	Single qubit Rotation gate around the axis \(\hat{y}\)
GateRZ(lmbda)	Single qubit Rotation gate around the axis \(\hat{z}\)

class mimiqcircuits.operations.gates.standard.rotations.GateRX(theta)

Bases: Gate

Single qubit Rotation gate around the axis \(\hat{x}\)

Matrix representation:

\[\begin{split}\operatorname{RX}(\theta) = \begin{pmatrix} \cos\frac{\theta}{2} & -i\sin\frac{\theta}{2} \\ -i\sin\frac{\theta}{2} & \cos\frac{\theta}{2} \end{pmatrix}\end{split}\]

Parameters:

theta – Rotation angle in radians.

Examples

>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta = Symbol('theta')
>>> GateRX(theta)
RX(theta)
>>> GateRX(theta).matrix()
[cos((1/2)*theta), -I*sin((1/2)*theta)]
[-I*sin((1/2)*theta), cos((1/2)*theta)]

>>> c = Circuit().push(GateRX(theta), 0)
>>> c
1-qubit circuit with 1 instruction:
└── RX(theta) @ q[0]

>>> GateRX(theta).power(2), GateRX(theta).inverse()
(RX(2*theta), RX(-theta))
>>> GateRX(theta).decompose()
1-qubit circuit with 1 instruction:
└── U(theta, (-1/2)*pi, (1/2)*pi, 0.0) @ q[0]

__init__(theta)

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.

isidentity()

class mimiqcircuits.operations.gates.standard.rotations.GateRY(theta)

Bases: Gate

Single qubit Rotation gate around the axis \(\hat{y}\)

Matrix representation:

\[\begin{split}\operatorname{RY}(\theta) = \begin{pmatrix} \cos\frac{\theta}{2} & -\sin\frac{\theta}{2} \\ \sin\frac{\theta}{2} & \cos\frac{\theta}{2} \end{pmatrix}\end{split}\]

Parameters:

theta (float) – Rotation angle in radians.

Examples

>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta = Symbol('theta')
>>> GateRY(theta)
RY(theta)
>>> GateRY(theta).matrix()
[cos((1/2)*theta), -sin((1/2)*theta)]
[sin((1/2)*theta), cos((1/2)*theta)]

>>> c = Circuit().push(GateRY(theta), 0)
>>> c
1-qubit circuit with 1 instruction:
└── RY(theta) @ q[0]

>>> GateRY(theta).power(2), GateRY(theta).inverse()
(RY(2*theta), RY(-theta))
>>> GateRY(theta).decompose()
1-qubit circuit with 1 instruction:
└── U(theta, 0, 0, 0.0) @ q[0]

__init__(theta)

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.

isidentity()

class mimiqcircuits.operations.gates.standard.rotations.GateRZ(lmbda)

Bases: Gate

Single qubit Rotation gate around the axis \(\hat{z}\)

Matrix representation:

\[\begin{split}\operatorname{RZ}(\lambda) = \begin{pmatrix} e^{-i\frac{\lambda}{2}} & 0 \\ 0 & e^{i\frac{\lambda}{2}} \end{pmatrix}\end{split}\]

Parameters:

lambda – Rotation angle in radians.

Examples

>>> from mimiqcircuits import *
>>> from symengine import *
>>> lmbda = Symbol('lambda')
>>> GateRZ(lmbda)
RZ(lambda)
>>> GateRZ(lmbda).matrix()
[exp(-1/2*I*lambda), 0]
[0, exp(1/2*I*lambda)]

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

>>> GateRZ(lmbda).power(2), GateRZ(lmbda).inverse()
(RZ(2*lambda), RZ(-lambda))
>>> GateRZ(lmbda).decompose()
1-qubit circuit with 1 instruction:
└── U(0, 0, lambda, (-1/2)*lambda) @ 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.

isidentity()

class mimiqcircuits.operations.gates.standard.rotations.GateR(theta, phi)

Bases: Gate

Single qubit Rotation gate around the axis \(\cos(\phi)\hat{x} + \sin(\phi)\hat{y}\).

Matrix representation:

\[\begin{split}\operatorname R(\theta,\phi) = \begin{pmatrix} \cos \frac{\theta}{2} & -i e^{-i\phi} \sin \frac{\theta}{2} \\ -i e^{i \phi} \sin \frac{\theta}{2} & \cos \frac{\theta}{2} \end{pmatrix}\end{split}\]

Parameters:

• theta (float) – The rotation angle in radians.

• phi (float) – The axis of rotation in radians.

Example

>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta, phi = symbols('theta phi')
>>> GateR(theta, phi)
R(theta, phi)
>>> GateR(theta, phi).matrix()
[cos((1/2)*theta), -I*exp(-I*phi)*sin((1/2)*theta)]
[-I*exp(I*phi)*sin((1/2)*theta), cos((1/2)*theta)]

>>> c = Circuit().push(GateR(theta, phi), 0)
>>> GateR(theta, phi).power(2), GateR(theta, phi).inverse()
(R(2*theta, phi), R(-theta, phi))
>>> GateR(theta, phi).decompose()
1-qubit circuit with 1 instruction:
└── U3(theta, phi + (-1/2)*pi, -phi + (1/2)*pi) @ q[0]

__init__(theta, phi)

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.