mimiqcircuits.operations.gates.standard.cs

Controlled-S and Controlled-SDG gates.

Classes

GateCS([num_controls, operation])	Two qubit Controlled-S gate.
GateCSDG([num_controls, operation])	Adjoint of two qubit Controlled-S gate.

class mimiqcircuits.operations.gates.standard.cs.GateCS(num_controls=None, operation=None, *args, **kwargs)

Bases: Control

Two qubit Controlled-S gate.

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

See Also GateS

Matrix representation::

\[\begin{split}\operatorname{CS} =\begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & i \end{pmatrix}\end{split}\]

Examples

>>> from mimiqcircuits import *
>>> GateCS(), GateCS().num_controls, GateCS().num_targets, GateCS().num_qubits
(CS, 1, 1, 2)
>>> GateCS().matrix()
[1.0, 0, 0, 0]
[0, 1.0, 0, 0]
[0, 0, 1.0, 0]
[0, 0, 0, 0.0 + 1.0*I]

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

>>> GateCS().power(2), GateCS().inverse()
(CZ, C(S†))
>>> GateCS().decompose()
2-qubit circuit with 1 instruction:
└── CU(0, 0, (1/2)*pi, 0.0) @ q[0], q[1]

__init__(num_controls=1, operation=None)

Initialize a CS gate.

class mimiqcircuits.operations.gates.standard.cs.GateCSDG(num_controls=None, operation=None, *args, **kwargs)

Bases: Control

Adjoint of two qubit Controlled-S gate.

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

Matrix representation:

\[\begin{split}\operatorname{CS}^{\dagger} = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & -i \end{pmatrix}\end{split}\]

Examples

>>> from mimiqcircuits import *
>>> GateCSDG(), GateCSDG().num_controls, GateCSDG().num_targets, GateCSDG().num_qubits
(C(S†), 1, 1, 2)
>>> GateCSDG().matrix()
[1.0, 0, 0, 0]
[0, 1.0, 0, 0]
[0, 0, 1.0, 0]
[0, 0, 0, 6.12323399573677e-17 - 1.0*I]

>>> c = Circuit().push(GateCSDG(), 0, 1)
>>> c
2-qubit circuit with 1 instruction:
└── C(S†) @ q[0], q[1]

>>> GateCSDG().power(2), GateCSDG().inverse()
(C((S†)**2), CS)
>>> GateCSDG().decompose()
2-qubit circuit with 1 instruction:
└── CU(0, 0, (-1/2)*pi, 0.0) @ q[0], q[1]

__init__(num_controls=1, operation=None)

Initialize a CSDG gate.