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from mimiqcircuits.operations.gates.standard.sx import GateSX, GateSXDG
from mimiqcircuits.operations.gates.standard.hadamard import GateH
from mimiqcircuits.operations.gates.standard.deprecated import GateU1
import mimiqcircuits as mc
from symengine import pi
[docs]
def GateCSX():
r"""Two qubit Controled-SX gate.
By convention, the first qubit is the control and second one is the
targets.
**Matrix representation:**
.. math::
\operatorname{CSX} =\begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & \frac{1+i}{2} & \frac{1-i}{2} \\
0 & 0 & \frac{1-i}{2} & \frac{1+i}{2}
\end{pmatrix}
Examples:
>>> from mimiqcircuits import *
>>> GateCSX(), GateCSX().num_controls, GateCSX().num_targets, GateCSX().num_qubits
(CSX, 1, 1, 2)
>>> GateCSX().matrix()
[1.0, 0, 0, 0]
[0, 1.0, 0, 0]
[0, 0, 0.5 + 0.5*I, 0.5 - 0.5*I]
[0, 0, 0.5 - 0.5*I, 0.5 + 0.5*I]
<BLANKLINE>
>>> c = Circuit().push(GateCSX(), 0, 1)
>>> c
2-qubit circuit with 1 instructions:
└── CSX @ q[0], q[1]
<BLANKLINE>
>>> GateCSX().power(2), GateCSX().inverse()
(CX, C(SX†))
>>> GateCSX().decompose()
2-qubit circuit with 4 instructions:
├── C(S†) @ q[0], q[1]
├── CH @ q[0], q[1]
├── C(S†) @ q[0], q[1]
└── CU(0, 0, 0, (1/4)*pi) @ q[0], q[1]
<BLANKLINE>
"""
return mc.Control(1, GateSX())
@mc.register_control_decomposition(1, mc.GateSX)
def _decompose_gatecsx(gate, circ, qubits, bits, zvars):
a, b = qubits
circ.push(GateH(), b)
circ.push(GateU1(pi / 2).control(1), a, b)
circ.push(GateH(), b)
return circ
[docs]
def GateCSXDG():
r"""Two qubit :math:`{CSX}^\dagger` gate.
**Matrix representation:**
.. math::
\operatorname{CSX}^{\dagger} =\begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & \frac{1-i}{2} & \frac{1+i}{2} \\
0 & 0 & \frac{1+i}{2} & \frac{1-i}{2}
\end{pmatrix}
Examples:
>>> from mimiqcircuits import *
>>> GateCSXDG(), GateCSXDG().num_controls, GateCSXDG().num_targets, GateCSXDG().num_qubits
(C(SX†), 1, 1, 2)
>>> GateCSXDG().matrix()
[1.0, 0, 0, 0]
[0, 1.0, 0, 0]
[0, 0, 0.5 - 0.5*I, 0.5 + 0.5*I]
[0, 0, 0.5 + 0.5*I, 0.5 - 0.5*I]
<BLANKLINE>
>>> c = Circuit().push(GateCSXDG(), 0, 1)
>>> c
2-qubit circuit with 1 instructions:
└── C(SX†) @ q[0], q[1]
<BLANKLINE>
>>> GateCSXDG().power(2), GateCSXDG().inverse()
(C((SX†)**2), CSX)
>>> GateCSXDG().decompose()
2-qubit circuit with 4 instructions:
├── CS @ q[0], q[1]
├── CH @ q[0], q[1]
├── CS @ q[0], q[1]
└── CU(0, 0, 0, (-1/4)*pi) @ q[0], q[1]
<BLANKLINE>
"""
return mc.Control(1, GateSXDG())
@mc.register_control_decomposition(1, mc.GateSXDG)
def _decompose_gatecsxdg(gate, circ, qubits, bits, zvars):
a, b = qubits
circ.push(GateH(), b)
circ.push(GateU1(-pi / 2).control(1), a, b)
circ.push(GateH(), b)
return circ
