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# Licensed under the Apache License, Version 2.0 (the "License");
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# http://www.apache.org/licenses/LICENSE-2.0
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import mimiqcircuits.operations.gates.gate as mcg
from mimiqcircuits.operations.utils import power_idempotent, control_one_defined
from mimiqcircuits.operations.gates.standard.phase import GateP
from mimiqcircuits.operations.gates.standard.u import GateU
import mimiqcircuits as mc
from symengine import pi, I, Matrix
[docs]
class GateX(mcg.Gate):
r""" Single qubit Pauli-X gate.
**Matrix representation:**
.. math::
\operatorname{X} = \begin{pmatrix}
0 & 1 \\
1 & 0
\end{pmatrix}
Examples:
>>> from mimiqcircuits import *
>>> GateX()
X
>>> GateX().matrix()
[0, 1.0]
[1.0, 0]
<BLANKLINE>
>>> c = Circuit().push(GateX(), 0)
>>> c
1-qubit circuit with 1 instructions:
└── X @ q[0]
<BLANKLINE>
>>> GateX().power(2), GateX().inverse()
(ID, X)
>>> GateX().decompose()
1-qubit circuit with 1 instructions:
└── U(pi, 0, pi, 0.0) @ q[0]
<BLANKLINE>
"""
_name = "X"
_num_qubits = 1
_qregsizes = [1]
[docs]
def inverse(self):
return self
def _power(self, p):
pmod = p % 2
# sqrt(X) = SX
if pmod == 1 / 2:
return mc.GateSX()
# SX * SX^3 = X * X = ID => SX^3 = SXDG
if pmod == 3 / 2:
return mc.GateSXDG()
# X^(2n) = ID
# X^(2n + 1) = X
return power_idempotent(self, p)
def _control(self, n):
return control_one_defined(n, self, mc.GateCX(), mc.GateCCX(), mc.GateC3X())
def _matrix(self):
return Matrix([[0, 1], [1, 0]])
def _decompose(self, circ, qubits, bits, zvars):
q = qubits[0]
circ.push(GateU(pi, 0, pi), q)
return circ
[docs]
class GateY(mcg.Gate):
r"""Single qubit Pauli-Y gate.
**Matrix representation:**
.. math::
\operatorname{Y} = \begin{pmatrix}
0 & -i \\
i & 0
\end{pmatrix}
Examples:
>>> from mimiqcircuits import *
>>> GateY()
Y
>>> GateY().matrix()
[0, -0.0 - 1.0*I]
[0.0 + 1.0*I, 0]
<BLANKLINE>
>>> c = Circuit().push(GateY(), 0)
>>> GateY().power(2), GateY().inverse()
(ID, Y)
>>> GateY().decompose()
1-qubit circuit with 1 instructions:
└── U(pi, (1/2)*pi, (1/2)*pi, 0.0) @ q[0]
<BLANKLINE>
"""
_name = "Y"
_num_qubits = 1
_qregsizes = [1]
[docs]
def inverse(self):
return self
def _power(self, p):
# Y^(2n) = ID
# Y^(2n + 1) = Y
return power_idempotent(self, p)
def _control(self, n):
return control_one_defined(n, self, mc.GateCY())
def _matrix(self):
return Matrix([[0, -I], [I, 0]])
def _decompose(self, circ, qubits, bits, zvars):
q = qubits[0]
circ.push(GateU(pi, pi / 2, pi / 2), q)
return circ
[docs]
class GateZ(mcg.Gate):
r"""Single qubit Pauli-Z gate.
**Matrix representation:**
.. math::
\operatorname{Z} = \begin{pmatrix}
1 & 0 \\
0 & -1
\end{pmatrix}
Examples:
>>> from mimiqcircuits import *
>>> GateZ()
Z
>>> GateZ().matrix()
[1.0, 0]
[0, -1.0]
<BLANKLINE>
>>> c = Circuit().push(GateZ(), 0)
>>> GateZ().power(2), GateZ().inverse()
(ID, Z)
>>> GateZ().decompose()
1-qubit circuit with 1 instructions:
└── P(pi) @ q[0]
<BLANKLINE>
"""
_name = "Z"
_num_qubits = 1
_qregsizes = [1]
[docs]
def inverse(self):
return self
def _power(self, p):
pmod = p % 2
# sqrt(Z) = S
if pmod == 1 / 2:
return mc.GateS()
# S * S^3 = Z * Z = ID => S^3 = SDG
if pmod == 3 / 2:
return mc.GateSDG()
# sqrt(S) = T
if pmod == 1 / 4:
return mc.GateT()
# T * T^7 = S^2 * S^2 = Z * Z = ID => T^7 = TDG
if pmod == 7 / 4:
return mc.GateTDG()
# Z^(2n) = ID
# Z^(2n + 1) = Z
return power_idempotent(self, p)
def _control(self, n):
return control_one_defined(n, self, mc.GateCZ())
def _matrix(self):
return Matrix([[1, 0], [0, -1]])
def _decompose(self, circ, qubits, bits, zvars):
q = qubits[0]
circ.push(GateP(pi), q)
return circ
