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from mimiqcircuits.operations.gates.standard.s import GateS, GateSDG
from mimiqcircuits.operations.gates.standard.cphase import GateCP
import mimiqcircuits as mc
from symengine import pi
[docs]
def GateCS():
r"""Two qubit Controlled-S gate.
By convention, the first qubit is the control and the second is
the target
See Also :func:`GateS`
**Matrix representation:**:
.. math::
\operatorname{CS} =\begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & i
\end{pmatrix}
Examples:
>>> from mimiqcircuits import *
>>> GateCS(), GateCS().num_controls, GateCS().num_targets, GateCS().num_qubits
(CS, 1, 1, 2)
>>> GateCS().matrix()
[1.0, 0, 0, 0]
[0, 1.0, 0, 0]
[0, 0, 1.0, 0]
[0, 0, 0, 0.0 + 1.0*I]
<BLANKLINE>
>>> c = Circuit().push(GateCS(), 0, 1)
>>> c
2-qubit circuit with 1 instructions:
└── CS @ q[0], q[1]
<BLANKLINE>
>>> GateCS().power(2), GateCS().inverse()
(CZ, C(S†))
>>> GateCS().decompose()
2-qubit circuit with 1 instructions:
└── CU(0, 0, (1/2)*pi, 0.0) @ q[0], q[1]
<BLANKLINE>
"""
return mc.Control(1, GateS())
@mc.register_control_decomposition(1, mc.GateS)
def _decompose_gatecs(gate, circ, qubits, bits, zvars):
a, b = qubits
circ.push(GateCP(pi / 2), a, b)
return circ
[docs]
def GateCSDG():
r"""Adjoint of two qubit Controlled-S gate.
By convention, the first qubit is the control and the second is
the target
**Matrix representation:**
.. math::
\operatorname{CS}^{\dagger} = \begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & -i
\end{pmatrix}
Examples:
>>> from mimiqcircuits import *
>>> GateCSDG(), GateCSDG().num_controls, GateCSDG().num_targets, GateCSDG().num_qubits
(C(S†), 1, 1, 2)
>>> GateCSDG().matrix()
[1.0, 0, 0, 0]
[0, 1.0, 0, 0]
[0, 0, 1.0, 0]
[0, 0, 0, 6.12323399573677e-17 - 1.0*I]
<BLANKLINE>
>>> c = Circuit().push(GateCSDG(), 0, 1)
>>> c
2-qubit circuit with 1 instructions:
└── C(S†) @ q[0], q[1]
<BLANKLINE>
>>> GateCSDG().power(2), GateCSDG().inverse()
(C((S†)**2), CS)
>>> GateCSDG().decompose()
2-qubit circuit with 1 instructions:
└── CU(0, 0, (-1/2)*pi, 0.0) @ q[0], q[1]
<BLANKLINE>
"""
return mc.Control(1, mc.GateSDG())
@mc.register_control_decomposition(1, mc.GateSDG)
def _decompose_gatecsdg(gate, circ, qubits, bits, zvars):
a, b = qubits
circ.push(GateCP(-pi / 2), a, b)
return circ
