mimiqcircuits.operations.gates.standard.crotations¶

Controlled-Rotation (CRX, CRY, CRZ) gates.

Classes

`GateCRX`([num_controls, operation])	Two qubit Controlled-RX gate.
`GateCRY`([num_controls, operation])	Two qubit Controlled-RY gate.
`GateCRZ`([num_controls, operation])	Two qubit Controlled-RZ gate.

class mimiqcircuits.operations.gates.standard.crotations.GateCRX(num_controls=None, operation=None, *args, **kwargs)[source]¶

Bases: Control

Two qubit Controlled-RX gate.

By convention, the first qubit is the control and the second is the target

See Also GateRX, GateCRY, GateCRZ

Matrix representation:

\[\begin{split}\operatorname{CRX}(\theta) = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & \cos\frac{\theta}{2} & -i\sin\frac{\theta}{2} \\ 0 & 0 & -i\sin\frac{\theta}{2} & \cos\frac{\theta}{2} \end{pmatrix}\end{split}\]

Parameters:: theta – The rotation angle in radians.

Examples

>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta = Symbol('theta')
>>> GateCRX(theta), GateCRX(theta).num_controls, GateCRX(theta).num_targets, GateCRX(theta).num_qubits
(CRX(theta), 1, 1, 2)
>>> GateCRX(theta).matrix()
[1.0, 0, 0, 0]
[0, 1.0, 0, 0]
[0, 0, cos((1/2)*theta), -I*sin((1/2)*theta)]
[0, 0, -I*sin((1/2)*theta), cos((1/2)*theta)]

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

>>> GateCRX(theta).power(2), GateCRX(theta).inverse()
(CRX(2*theta), CRX(-theta))
>>> GateCRX(theta).decompose()
2-qubit circuit with 5 instructions:
├── P((1/2)*pi) @ q[1]
├── CX @ q[0], q[1]
├── U((-1/2)*theta, 0, 0, 0.0) @ q[1]
├── CX @ q[0], q[1]
└── U((1/2)*theta, (-1/2)*pi, 0, 0.0) @ q[1]

__init__(theta_or_num_controls, num_controls_or_operation=None, operation=None)[source]¶

Initialize a CRX gate.

Parameters:

theta_or_num_controls – The rotation angle in radians when called directly, or num_controls when called from Control’s canonical creation.
num_controls_or_operation – Ignored when called directly, or the GateRX operation when called from Control’s canonical creation.
operation – Ignored (for compatibility).

class mimiqcircuits.operations.gates.standard.crotations.GateCRY(num_controls=None, operation=None, *args, **kwargs)[source]¶

Bases: Control

Two qubit Controlled-RY gate.

By convention, the first qubit is the control and the second is the target

See Also GateRY, GateCRX, GateCRZ

Matrix representation:

\[\begin{split}\operatorname{CRY}(\theta) = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & \cos\frac{\theta}{2} & -\sin\frac{\theta}{2} \\ 0 & 0 & \sin\frac{\theta}{2} & \cos\frac{\theta}{2} \end{pmatrix}\end{split}\]

Parameters:: theta – The rotation angle in radians.

Examples

>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta = Symbol('theta')
>>> GateCRY(theta), GateCRY(theta).num_controls, GateCRY(theta).num_targets, GateCRY(theta).num_qubits
(CRY(theta), 1, 1, 2)
>>> GateCRY(theta).matrix()
[1.0, 0, 0, 0]
[0, 1.0, 0, 0]
[0, 0, cos((1/2)*theta), -sin((1/2)*theta)]
[0, 0, sin((1/2)*theta), cos((1/2)*theta)]

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

>>> GateCRY(theta).power(2), GateCRY(theta).inverse()
(CRY(2*theta), CRY(-theta))
>>> GateCRY(theta).decompose()
2-qubit circuit with 4 instructions:
├── RY((1/2)*theta) @ q[1]
├── CX @ q[0], q[1]
├── RY((-1/2)*theta) @ q[1]
└── CX @ q[0], q[1]

__init__(theta_or_num_controls, num_controls_or_operation=None, operation=None)[source]¶

Initialize a CRY gate.

Parameters:

theta_or_num_controls – The rotation angle in radians when called directly, or num_controls when called from Control’s canonical creation.
num_controls_or_operation – Ignored when called directly, or the GateRY operation when called from Control’s canonical creation.
operation – Ignored (for compatibility).

class mimiqcircuits.operations.gates.standard.crotations.GateCRZ(num_controls=None, operation=None, *args, **kwargs)[source]¶

Bases: Control

Two qubit Controlled-RZ gate.

By convention, the first qubit is the control and the second is the target

See Also GateRZ, GateCRX, GateCRY

Matrix representation:

\[\begin{split}\operatorname{CRZ}(\lambda) = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & e^{-i\frac{\lambda}{2}} & 0 \\ 0 & 0 & 0 & e^{i\frac{\lambda}{2}} \end{pmatrix}\end{split}\]

Parameters:: lmbda – The rotation angle in radians.

Examples

>>> from mimiqcircuits import *
>>> from symengine import *
>>> lmbda = Symbol('lambda')
>>> GateCRZ(lmbda), GateCRZ(lmbda).num_controls, GateCRZ(lmbda).num_targets, GateCRZ(lmbda).num_qubits
(CRZ(lambda), 1, 1, 2)
>>> GateCRZ(lmbda).matrix()
[1.0, 0, 0, 0]
[0, 1.0, 0, 0]
[0, 0, exp(-1/2*I*lambda), 0]
[0, 0, 0, exp(1/2*I*lambda)]

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

>>> GateCRZ(lmbda).power(2), GateCRZ(lmbda).inverse()
(CRZ(2*lambda), CRZ(-lambda))
>>> GateCRZ(lmbda).decompose()
2-qubit circuit with 4 instructions:
├── RZ((1/2)*lambda) @ q[1]
├── CX @ q[0], q[1]
├── RZ((-1/2)*lambda) @ q[1]
└── CX @ q[0], q[1]

__init__(lmbda_or_num_controls, num_controls_or_operation=None, operation=None)[source]¶

Initialize a CRZ gate.

Parameters:

lmbda_or_num_controls – The rotation angle in radians when called directly, or num_controls when called from Control’s canonical creation.
num_controls_or_operation – Ignored when called directly, or the GateRZ operation when called from Control’s canonical creation.
operation – Ignored (for compatibility).