Source code for mimiqcircuits.operations.gates.standard.hadamard

#
# Copyright © 2022-2023 University of Strasbourg. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#

import mimiqcircuits as mc
from mimiqcircuits.operations.utils import power_idempotent
from mimiqcircuits.matrices import gphasepi, umatrixpi
from mimiqcircuits.operations.utils import control_one_defined
from symengine import pi, sqrt, Matrix


[docs] class GateH(mc.Gate): r"""Single qubit Hadamard gate. **Matrix representation:** .. math:: \operatorname{H} = \frac{1}{\sqrt{2}} \begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix} Examples: >>> from mimiqcircuits import * >>> GateH() H >>> GateH().matrix() [0.707106781186548, 0.707106781186548] [0.707106781186548, -0.707106781186548] <BLANKLINE> >>> c = Circuit().push(GateH(), 0) >>> c 1-qubit circuit with 1 instructions: └── H @ q[0] <BLANKLINE> >>> GateH().power(2), GateH().inverse() (ID, H) >>> GateH().decompose() 1-qubit circuit with 1 instructions: └── U((1/2)*pi, 0, pi, 0.0) @ q[0] <BLANKLINE> """ _name = "H" _num_qubits = 1 _qregsizes = [1]
[docs] def inverse(self): return self
def _power(self, p): # H^(2n) = ID # H^(2n+1) = H return power_idempotent(self, p) def _control(self, n): return control_one_defined(self, n) def _matrix(self): return Matrix([[1, 1], [1, -1]]) / sqrt(2) def _decompose(self, circ, qubits, bits): q = qubits[0] circ.push(mc.GateU(pi/2, 0, pi), q) return circ