#
# Copyright © 2022-2024 University of Strasbourg. All Rights Reserved.
# Copyright © 2023-2025 QPerfect. 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
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
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from symengine import pi
import mimiqcircuits as mc
[docs]
def GateSX():
r"""Single qubit :math:`\sqrt{X}` gate.
**Matrix representation:**
.. math::
\sqrt{\operatorname{X}} = \frac{1}{2} \begin{pmatrix}
1+i & 1-i \\
1-i & 1+i\\
\end{pmatrix}
Examples:
>>> from mimiqcircuits import *
>>> GateSX()
SX
>>> GateSX().matrix()
[0.5 + 0.5*I, 0.5 - 0.5*I]
[0.5 - 0.5*I, 0.5 + 0.5*I]
<BLANKLINE>
>>> c = Circuit().push(GateSX(), 0)
>>> c
1-qubit circuit with 1 instructions:
└── SX @ q[0]
<BLANKLINE>
>>> GateSX().power(2), GateSX().inverse()
(X, SX†)
>>> GateSX().decompose()
1-qubit circuit with 4 instructions:
├── S† @ q[0]
├── H @ q[0]
├── S† @ q[0]
└── U(0, 0, 0, (1/4)*pi) @ q[0]
<BLANKLINE>
"""
return mc.Power(mc.GateX(), 1 / 2)
mc.register_power_alias(mc.GateX, 1 / 2, "SX")
@mc.register_power_decomposition(mc.GateX, 1 / 2)
def _decompose_gatesx(self, circ, qubits, bits, zvars):
q = qubits[0]
circ.push(mc.GateSDG(), q)
circ.push(mc.GateH(), q)
circ.push(mc.GateSDG(), q)
circ.push(mc.GateU(0, 0, 0, pi / 4), q)
return circ
[docs]
def GateSXDG():
r"""Single qubit :math:`\sqrt{X}^\dagger` gate (conjugate transpose of the :math:`\sqrt{X}` gate).
**Matrix representation:**
.. math::
\sqrt{\operatorname{X}}^\dagger = \frac{1}{2} \begin{pmatrix}
1-i & 1+i \\
1+i & 1-i\\
\end{pmatrix}
Examples:
>>> from mimiqcircuits import *
>>> GateSXDG()
SX†
>>> GateSXDG().matrix()
[0.5 - 0.5*I, 0.5 + 0.5*I]
[0.5 + 0.5*I, 0.5 - 0.5*I]
<BLANKLINE>
>>> c = Circuit().push(GateSXDG(), 0)
>>> c
1-qubit circuit with 1 instructions:
└── SX† @ q[0]
<BLANKLINE>
>>> GateSXDG().power(2), GateSXDG().inverse()
((SX†)**2, SX)
>>> GateSXDG().decompose()
1-qubit circuit with 4 instructions:
├── S @ q[0]
├── H @ q[0]
├── S @ q[0]
└── U(0, 0, 0, (-1/4)*pi) @ q[0]
<BLANKLINE>
"""
return mc.Inverse(GateSX())
@mc.register_inverse_decomposition((mc.Power, mc.GateX, 1 / 2))
def _decompose_gatesxdg(self, circ, qubits, bits, zvars):
q = qubits[0]
circ.push(mc.GateS(), q)
circ.push(mc.GateH(), q)
circ.push(mc.GateS(), q)
circ.push(mc.GateU(0, 0, 0, -pi / 4), q)
return circ
