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"""Controlled-Rotation (CRX, CRY, CRZ) gates."""
from mimiqcircuits.operations.gates.standard.cpauli import GateCX
from mimiqcircuits.operations.gates.standard.u import GateU
from mimiqcircuits.operations.gates.standard.s import GateS
from mimiqcircuits.operations.gates.standard.rotations import GateRX, GateRY, GateRZ
import mimiqcircuits as mc
from mimiqcircuits.operations.gates.standard._angles import NEG_PI_2
[docs]
@mc.canonical_control(1, GateRX)
class GateCRX(mc.Control):
r"""Two qubit Controlled-RX gate.
By convention, the first qubit is the control and the second is
the target
See Also :class:`GateRX`, :class:`GateCRY`, :class:`GateCRZ`
**Matrix representation:**
.. math::
\operatorname{CRX}(\theta) = \begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & \cos\frac{\theta}{2} & -i\sin\frac{\theta}{2} \\
0 & 0 & -i\sin\frac{\theta}{2} & \cos\frac{\theta}{2}
\end{pmatrix}
Parameters:
theta: The rotation angle in radians.
Examples:
>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta = Symbol('theta')
>>> GateCRX(theta), GateCRX(theta).num_controls, GateCRX(theta).num_targets, GateCRX(theta).num_qubits
(CRX(theta), 1, 1, 2)
>>> GateCRX(theta).matrix()
[1.0, 0, 0, 0]
[0, 1.0, 0, 0]
[0, 0, cos((1/2)*theta), -I*sin((1/2)*theta)]
[0, 0, -I*sin((1/2)*theta), cos((1/2)*theta)]
<BLANKLINE>
>>> c = Circuit().push(GateCRX(theta), 0, 1)
>>> c
2-qubit circuit with 1 instruction:
└── CRX(theta) @ q[0], q[1]
<BLANKLINE>
>>> GateCRX(theta).power(2), GateCRX(theta).inverse()
(CRX(2*theta), CRX(-theta))
>>> GateCRX(theta).decompose()
2-qubit circuit with 5 instructions:
├── S @ q[1]
├── CX @ q[0], q[1]
├── U((-1/2)*theta, 0, 0, 0.0) @ q[1]
├── CX @ q[0], q[1]
└── U((1/2)*theta, (-1/2)*pi, 0, 0.0) @ q[1]
<BLANKLINE>
"""
[docs]
def __init__(
self, theta_or_num_controls, num_controls_or_operation=None, operation=None
):
"""Initialize a CRX gate.
Args:
theta_or_num_controls: The rotation angle in radians when called directly,
or num_controls when called from Control's canonical creation.
num_controls_or_operation: Ignored when called directly, or the GateRX
operation when called from Control's canonical creation.
operation: Ignored (for compatibility).
"""
# Detect if called from Control's canonical creation: Control(1, GateRX(theta))
# In that case, theta_or_num_controls is int and num_controls_or_operation is GateRX
if isinstance(theta_or_num_controls, int) and isinstance(
num_controls_or_operation, GateRX
):
theta = num_controls_or_operation.theta
else:
theta = theta_or_num_controls
super().__init__(1, GateRX(theta))
@mc.register_control_decomposition(1, mc.GateRX)
def _decompose_gatecrx(gate, circ, qubits, bits, zvars):
c, t = qubits
theta = gate.op.theta
circ.push(GateS(), t)
circ.push(GateCX(), c, t)
circ.push(GateU(-theta / 2, 0, 0), t)
circ.push(GateCX(), c, t)
circ.push(GateU(theta / 2, NEG_PI_2, 0), t)
return circ
[docs]
@mc.canonical_control(1, GateRY)
class GateCRY(mc.Control):
r"""Two qubit Controlled-RY gate.
By convention, the first qubit is the control and the second is
the target
See Also :class:`GateRY`, :class:`GateCRX`, :class:`GateCRZ`
**Matrix representation:**
.. math::
\operatorname{CRY}(\theta) = \begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & \cos\frac{\theta}{2} & -\sin\frac{\theta}{2} \\
0 & 0 & \sin\frac{\theta}{2} & \cos\frac{\theta}{2}
\end{pmatrix}
Parameters:
theta: The rotation angle in radians.
Examples:
>>> from mimiqcircuits import *
>>> from symengine import *
>>> theta = Symbol('theta')
>>> GateCRY(theta), GateCRY(theta).num_controls, GateCRY(theta).num_targets, GateCRY(theta).num_qubits
(CRY(theta), 1, 1, 2)
>>> GateCRY(theta).matrix()
[1.0, 0, 0, 0]
[0, 1.0, 0, 0]
[0, 0, cos((1/2)*theta), -sin((1/2)*theta)]
[0, 0, sin((1/2)*theta), cos((1/2)*theta)]
<BLANKLINE>
>>> c = Circuit().push(GateCRY(theta), 0, 1)
>>> c
2-qubit circuit with 1 instruction:
└── CRY(theta) @ q[0], q[1]
<BLANKLINE>
>>> GateCRY(theta).power(2), GateCRY(theta).inverse()
(CRY(2*theta), CRY(-theta))
>>> GateCRY(theta).decompose()
2-qubit circuit with 4 instructions:
├── RY((1/2)*theta) @ q[1]
├── CX @ q[0], q[1]
├── RY((-1/2)*theta) @ q[1]
└── CX @ q[0], q[1]
<BLANKLINE>
"""
[docs]
def __init__(
self, theta_or_num_controls, num_controls_or_operation=None, operation=None
):
"""Initialize a CRY gate.
Args:
theta_or_num_controls: The rotation angle in radians when called directly,
or num_controls when called from Control's canonical creation.
num_controls_or_operation: Ignored when called directly, or the GateRY
operation when called from Control's canonical creation.
operation: Ignored (for compatibility).
"""
# Detect if called from Control's canonical creation: Control(1, GateRY(theta))
if isinstance(theta_or_num_controls, int) and isinstance(
num_controls_or_operation, GateRY
):
theta = num_controls_or_operation.theta
else:
theta = theta_or_num_controls
super().__init__(1, GateRY(theta))
@mc.register_control_decomposition(1, mc.GateRY)
def _decompose_gatecry(gate, circ, qubits, bits, zvars):
c, t = qubits
theta = gate.op.theta
circ.push(GateRY(theta / 2), t)
circ.push(GateCX(), c, t)
circ.push(GateRY(-theta / 2), t)
circ.push(GateCX(), c, t)
return circ
[docs]
@mc.canonical_control(1, GateRZ)
class GateCRZ(mc.Control):
r"""Two qubit Controlled-RZ gate.
By convention, the first qubit is the control and the second is
the target
See Also :class:`GateRZ`, :class:`GateCRX`, :class:`GateCRY`
**Matrix representation:**
.. math::
\operatorname{CRZ}(\lambda) = \begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & e^{-i\frac{\lambda}{2}} & 0 \\
0 & 0 & 0 & e^{i\frac{\lambda}{2}}
\end{pmatrix}
Parameters:
lmbda: The rotation angle in radians.
Examples:
>>> from mimiqcircuits import *
>>> from symengine import *
>>> lmbda = Symbol('lambda')
>>> GateCRZ(lmbda), GateCRZ(lmbda).num_controls, GateCRZ(lmbda).num_targets, GateCRZ(lmbda).num_qubits
(CRZ(lambda), 1, 1, 2)
>>> GateCRZ(lmbda).matrix()
[1.0, 0, 0, 0]
[0, 1.0, 0, 0]
[0, 0, exp(-1/2*I*lambda), 0]
[0, 0, 0, exp(1/2*I*lambda)]
<BLANKLINE>
>>> c = Circuit().push(GateCRZ(lmbda), 0, 1)
>>> c
2-qubit circuit with 1 instruction:
└── CRZ(lambda) @ q[0], q[1]
<BLANKLINE>
>>> GateCRZ(lmbda).power(2), GateCRZ(lmbda).inverse()
(CRZ(2*lambda), CRZ(-lambda))
>>> GateCRZ(lmbda).decompose()
2-qubit circuit with 4 instructions:
├── RZ((1/2)*lambda) @ q[1]
├── CX @ q[0], q[1]
├── RZ((-1/2)*lambda) @ q[1]
└── CX @ q[0], q[1]
<BLANKLINE>
"""
[docs]
def __init__(
self, lmbda_or_num_controls, num_controls_or_operation=None, operation=None
):
"""Initialize a CRZ gate.
Args:
lmbda_or_num_controls: The rotation angle in radians when called directly,
or num_controls when called from Control's canonical creation.
num_controls_or_operation: Ignored when called directly, or the GateRZ
operation when called from Control's canonical creation.
operation: Ignored (for compatibility).
"""
# Detect if called from Control's canonical creation: Control(1, GateRZ(lmbda))
if isinstance(lmbda_or_num_controls, int) and isinstance(
num_controls_or_operation, GateRZ
):
lmbda = num_controls_or_operation.lmbda
else:
lmbda = lmbda_or_num_controls
super().__init__(1, GateRZ(lmbda))
@mc.register_control_decomposition(1, mc.GateRZ)
def _decompose_gatecrz(gate, circ, qubits, bits, zvars):
c, t = qubits
lmbda = gate.op.lmbda
circ.push(GateRZ(lmbda / 2), t)
circ.push(GateCX(), c, t)
circ.push(GateRZ(-lmbda / 2), t)
circ.push(GateCX(), c, t)
return circ