Hadamard

from qualtran import Bloq, CompositeBloq, BloqBuilder, Signature, Register
from qualtran import QBit, QInt, QUInt, QAny
from qualtran.drawing import show_bloq, show_call_graph, show_counts_sigma
from typing import *
import numpy as np
import sympy
import cirq

Hadamard

The Hadamard gate

This converts between the X and Z basis.

\[\begin{split} \begin{aligned} H |0\rangle = |+\rangle \\ H |-\rangle = |1\rangle \end{aligned} \end{split}\]

Registers

• q: The qubit

from qualtran.bloqs.basic_gates import Hadamard

Example Instances

hadamard = Hadamard()

Graphical Signature

from qualtran.drawing import show_bloqs
show_bloqs([hadamard],
           ['`hadamard`'])

CHadamard

The controlled Hadamard gate

Registers

• ctrl: The control qubit.

• target: The target qubit.

from qualtran.bloqs.basic_gates import CHadamard

Example Instances

chadamard = Hadamard().controlled()
assert isinstance(chadamard, CHadamard)

Graphical Signature

from qualtran.drawing import show_bloqs
show_bloqs([chadamard],
           ['`chadamard`'])

show_bloq(chadamard, 'musical_score')

Specialty circuits

The CHadamard bloq is atomic and cannot be decomposed with .decompose_bloq(). An actual implementation on an error-corrected quantum computer will likely be architecture-dependent. A naive circuit for CHadamard can be found using Cirq.

circuit = cirq.Circuit(cirq.decompose_multi_controlled_rotation(
    cirq.unitary(cirq.H),
    controls=[cirq.NamedQubit('ctrl')],
    target=cirq.NamedQubit('q'),
))
circuit

ctrl: ───S─────────────────────────────@───────────────────────────────────@───────────────────────────
                                       │                                   │
         ┌                         ┐   │   ┌                           ┐   │   ┌                   ┐
q: ──────│0.707+0.707j 0.   +0.j   │───X───│ 0.653+0.653j -0.271+0.271j│───X───│0.-0.924j 0.-0.383j│───
         │0.   +0.j    0.707-0.707j│       │ 0.271+0.271j  0.653-0.653j│       │0.-0.383j 0.+0.924j│
         └                         ┘       └                           ┘       └                   ┘