mimiqcircuits.operations.gates.standard.chadamard

Controlled-Hadamard gate.

Classes

GateCH([num_controls, operation])

Two qubit Controlled-Hadamard gate.

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

Bases: Control

Two qubit Controlled-Hadamard gate.

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

Matrix representation:

\[\begin{split}\operatorname{CH} = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\ 0 & 0 & \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \end{pmatrix}\end{split}\]

Examples

>>> from mimiqcircuits import *
>>> GateCH(), GateCH().num_controls, GateCH().num_targets, GateCH().num_qubits
(CH, 1, 1, 2)
>>> GateCH().matrix()
[1.0, 0, 0, 0]
[0, 1.0, 0, 0]
[0, 0, 0.707106781186548, 0.707106781186548]
[0, 0, 0.707106781186548, -0.707106781186548]

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

>>> GateCH().power(2), GateCH().inverse()
(CID, CH)
>>> GateCH().decompose()
2-qubit circuit with 7 instructions:
├── S @ q[1]
├── H @ q[1]
├── T @ q[1]
├── CX @ q[0], q[1]
├── T† @ q[1]
├── H @ q[1]
└── S† @ q[1]

__init__(num_controls=1, operation=None)

Initialize a CH gate.