def hadamard_axbxc(gate) -> QCircuit:
"""
Decompose 1 control parametrized hadamard into single qubit rotation and CNOT.
Parameters
----------
gate:
the gate
Returns
-------
QCircuit, the result of compilation.
"""
if not isinstance(gate, PowerGateImpl) or gate.name not in [
'H', 'h', 'hadamard'
]:
return QCircuit.wrap_gate(gate)
power = gate.parameter
target = gate.target
a = power.wrap(a_calc)
b = power.wrap(b_calc)
theta = power.wrap(theta_calc)
phase = power * jnp.pi / 2
result = QCircuit()
result += Rz((a - b) / 2, target)
result += CNOT(gate.control, target)
result += Rz(-(a + b) / 2, target)
result += Ry(-theta / 2, target)
result += CNOT(gate.control, target)
result += Ry(theta / 2, target)
result += Rz(a, target)
result += Phase(numpy.pi * power / 2, gate.control)
return result
def compile_power_base(gate):
"""
Base case of compile_power_gate: convert a 1-qubit parametrized power gate into rotation gates.
Parameters
----------
gate:
the gate.
Returns
-------
A QCircuit; the result of compilation.
"""
if not isinstance(gate, PowerGateImpl):
return QCircuit.wrap_gate(gate)
if gate.is_controlled():
return QCircuit.wrap_gate(gate)
power = gate.power
if gate.name.lower() in ['h', 'hadamard']:
### off by global phase of Exp[ pi power /2]
theta = power * numpy.pi
result = QCircuit()
result += Ry(angle=-numpy.pi / 4, target=gate.target)
result += Rz(angle=theta, target=gate.target)
result += Ry(angle=numpy.pi / 4, target=gate.target)
elif gate.name == 'X':
### off by global phase of Exp[ pi power /2]
'''
if we wanted to do it formally we would use the following
a=-numpy.pi/2
b=numpy.pi/2
theta = power*numpy.pi
result = QCircuit()
result+= Rz(angle=b,target=gate.target)
result+= Ry(angle=theta,target=gate.target)
result+= Rz(angle=a,target=gate.target)
'''
result = Rx(angle=power * numpy.pi, target=gate.target)
elif gate.name == 'Y':
### off by global phase of Exp[ pi power /2]
theta = power * numpy.pi
result = QCircuit()
result += Ry(angle=theta, target=gate.target)
elif gate.name == 'Z':
### off by global phase of Exp[ pi power /2]
a = 0
b = power * numpy.pi
theta = 0
result = QCircuit()
result += Rz(angle=b, target=gate.target)
else:
raise TequilaException('passed a gate with name ' + gate.name +
', which cannot be handled!')
return result
def hadamard_base(gate) -> QCircuit:
"""
base case for hadamard compilation; returns powers of hadamard as sequence of single qubit rotations.
Parameters
----------
gate:
the gate.
Returns
-------
A QCircuit; the result of compilation.
"""
if not isinstance(gate, PowerGateImpl) or gate.name not in [
'H', 'h', 'hadamard'
]:
return QCircuit.wrap_gate(gate)
power = gate.parameter
a = power.wrap(a_calc)
b = power.wrap(b_calc)
theta = power.wrap(theta_calc)
result = QCircuit()
result += Rz(angle=b, target=gate.target)
result += Ry(angle=theta, target=gate.target)
result += Rz(angle=a, target=gate.target)
return result
def test_basic_gates():
I = sympy.I
cos = sympy.cos
sin = sympy.sin
exp = sympy.exp
BS = QubitWaveFunction.from_int
angle = sympy.pi
gates = [
X(0),
Y(0),
Z(0),
Rx(target=0, angle=angle),
Ry(target=0, angle=angle),
Rz(target=0, angle=angle),
H(0)
]
results = [
BS(1), I * BS(1),
BS(0),
cos(-angle / 2) * BS(0) + I * sin(-angle / 2) * BS(1),
cos(-angle / 2) * BS(0) + I * sin(-angle / 2) * I * BS(1),
exp(-I * angle / 2) * BS(0), 1 / sympy.sqrt(2) * (BS(0) + BS(1))
]
for i, g in enumerate(gates):
wfn = simulate(g, backend="symbolic", variables={angle: sympy.pi})
assert (wfn == strip_sympy_zeros(results[i]))
def test_consistency():
angle = numpy.pi / 2
cpairs = [(CNOT(target=0, control=1), X(target=0, control=1)),
(Ry(target=0, angle=numpy.pi),
Rz(target=0, angle=4 * numpy.pi) + X(target=0)),
(Rz(target=0,
angle=numpy.pi), Rz(target=0, angle=numpy.pi) + Z(target=0)),
(Rz(target=0, angle=angle),
Rz(target=0, angle=angle / 2) + Rz(target=0, angle=angle / 2)),
(Rx(target=0, angle=angle),
Rx(target=0, angle=angle / 2) + Rx(target=0, angle=angle / 2)),
(Ry(target=0, angle=angle),
Ry(target=0, angle=angle / 2) + Ry(target=0, angle=angle / 2))]
for c in cpairs:
print("circuit=", c[0], "\n", c[1])
wfn1 = simulate(c[0], backend="symbolic")
wfn2 = simulate(c[1], backend="symbolic")
assert (numpy.isclose(wfn1.inner(wfn2), 1.0))
def change_basis(target, axis=None, name=None, daggered=False):
"""
helper function; returns circuit that performs change of basis.
Parameters
----------
target:
the qubit having its basis changed
axis:
The axis of rotation to shift into.
daggered: bool:
adjusts the sign of the gate if axis = 1, I.E, change of basis about Y axis.
Returns
-------
QCircuit that performs change of basis on target qubit onto desired axis
"""
if axis is None and name is None:
raise TequilaException('axis or name must be given.')
if name:
name = name.lower()
if name in ['h', 'hadamard'] and daggered:
return Ry(angle=numpy.pi / 4, target=target)
elif name in ['h', 'hadamard']:
return Ry(angle=-numpy.pi / 4, target=target)
else:
name_to_axis = {'rx': 0, 'ry': 1, 'rz': 2}
axis = name_to_axis.get(name, name)
if isinstance(axis, str):
axis = RotationGateImpl.string_to_axis[axis.lower()]
if axis == 0 and daggered:
return Ry(angle=numpy.pi / 2, target=target)
elif axis == 0:
return Ry(angle=-numpy.pi / 2, target=target)
elif axis == 1 and daggered:
return Rx(angle=-numpy.pi / 2, target=target)
elif axis == 1:
return Rx(angle=numpy.pi / 2, target=target)
else:
return QCircuit()
def compile_ch(gate: QGateImpl) -> QCircuit:
"""
Compile CH gates into its equivalent:
CH = Ry(0.25pi) CZ Ry(-0.25pi)
Parameters
----------
gate:
the gate.
Returns
-------
QCircuit, the result of compilation.
"""
if gate.name.lower() == "h" and gate.is_controlled():
return Ry(target=gate.target, control=None, angle=-numpy.pi / 4) \
+ Z(target=gate.target, control=gate.control, power=gate.power if gate.is_parametrized() else None) \
+ Ry(target=gate.target, control=None, angle=numpy.pi / 4)
else:
return QCircuit.wrap_gate(gate)
def create_sub_circ(self, gate, control_bit, target_bit):
sub_circ = None
if gate == "CNOT":
sub_circ = CNOT(control=control_bit, target=target_bit)
elif gate == "aCNOT":
sub_circ = X(control_bit)
sub_circ += CNOT(control=control_bit, target=target_bit)
sub_circ += X(control_bit)
elif gate == "CROT":
a_angle = self.coefficients[self.c_i]
sa = sympy.Symbol(a_angle)
self.c_i += 1
sub_circ = Ry(control=control_bit,
target=target_bit,
angle=SympyVariable(sa))
elif gate == "aCROT":
a_angle = self.coefficients[self.c_i]
sa = sympy.Symbol(a_angle)
self.c_i += 1
sub_circ = X(control_bit)
sub_circ += Ry(control=control_bit,
target=target_bit,
angle=SympyVariable(sa))
sub_circ += X(control_bit)
elif gate == "X":
sub_circ = X(target_bit)
elif gate == "ROT":
a_angle = self.coefficients[self.c_i]
self.c_i += 1
sub_circ = Ry(control=None,
target=target_bit,
angle=SympyVariable(sympy.Symbol(a_angle)))
return sub_circ
def hadamard_axbxc(gate) -> QCircuit:
if not isinstance(gate, PowerGateImpl) or gate.name not in [
'H', 'h', 'hadamard'
]:
return QCircuit.wrap_gate(gate)
power = gate.parameter
target = gate.target
a = power.wrap(a_calc)
b = power.wrap(b_calc)
theta = power.wrap(theta_calc)
phase = power * jnp.pi / 2
result = QCircuit()
result += Rz((a - b) / 2, target)
result += CNOT(gate.control, target)
result += Rz(-(a + b) / 2, target)
result += Ry(-theta / 2, target)
result += CNOT(gate.control, target)
result += Ry(theta / 2, target)
result += Rz(a, target)
result += Phase(numpy.pi * power / 2, gate.control)
return result
def hadamard_base(gate) -> QCircuit:
if not isinstance(gate, PowerGateImpl) or gate.name not in [
'H', 'h', 'hadamard'
]:
return QCircuit.wrap_gate(gate)
power = gate.parameter
a = power.wrap(a_calc)
b = power.wrap(b_calc)
theta = power.wrap(theta_calc)
result = QCircuit()
result += Rz(angle=b, target=gate.target)
result += Ry(angle=theta, target=gate.target)
result += Rz(angle=a, target=gate.target)
return result
def test_unitary_gate_u2(ctrl, phi, lambd):
"""
Test some equivalences for u2 gate
Since u2(\\phi, \\lambda) = Rz(\\phi)Ry(\\pi/2)Rz(\\lambda)
"""
c_u2 = u2(phi=phi, lambd=lambd, target=0, control=ctrl)
c_equiv = Rz(target=0, control=ctrl, angle=lambd) + \
Ry(target=0, control=ctrl, angle=numpy.pi / 2) + \
Rz(target=0, control=ctrl, angle=phi)
if ctrl is not None:
c_u2 = X(target=ctrl) + c_u2
c_equiv = X(target=ctrl) + c_equiv
wfn1 = simulate(c_u2, backend="symbolic")
wfn2 = simulate(c_equiv, backend="symbolic")
assert (numpy.isclose(wfn1.inner(wfn2), 1.0))
def compile_power_base(gate):
if not isinstance(gate, PowerGateImpl):
return QCircuit.wrap_gate(gate)
power = gate.parameter
if gate.name in ['H', 'h', 'Hadamard', 'hadamard']:
return compile_h_power(gate=gate)
if gate.name == 'X':
### off by global phase of Exp[ pi power /2]
'''
if we wanted to do it formally we would use the following
a=-numpy.pi/2
b=numpy.pi/2
theta = power*numpy.pi
result = QCircuit()
result+= Rz(angle=b,target=gate.target)
result+= Ry(angle=theta,target=gate.target)
result+= Rz(angle=a,target=gate.target)
'''
result = Rx(angle=power * numpy.pi, target=gate.target)
elif gate.name == 'Y':
### off by global phase of Exp[ pi power /2]
theta = power * numpy.pi
result = QCircuit()
result += Ry(angle=theta, target=gate.target)
elif gate.name == 'Z':
### off by global phase of Exp[ pi power /2]
a = 0
b = power * numpy.pi
theta = 0
result = QCircuit()
result += Rz(angle=b, target=gate.target)
else:
raise TequilaException('passed a gate with name ' + gate.name +
', which cannot be handled!')
return result
def get_axbxc_decomp(gate):
"""
Break down single controlled parametrized power gates into CNOT and rotations.
Parameters
----------
gate:
the gate.
Returns
-------
QCircuit; the result of compilation.
"""
if not isinstance(gate, PowerGateImpl) or gate.name not in ['X', 'Y', 'Z']:
return QCircuit.wrap_gate(gate)
power = gate.parameter
target = gate.target
result = QCircuit()
if gate.name == 'X':
a = -numpy.pi / 2
b = numpy.pi / 2
theta = power * numpy.pi
'''
result+=Phase(numpy.pi*power/2,gate.control)
result+=Rz(-(a-b)/2,target)
result+=CNOT(gate.control,target)
#result+=Rz(-(a+b)/2,target)
result+=Ry(-theta/2,target)
result+=CNOT(gate.control,target)
result+=Ry(theta/2,target)
result+=Rz(a,target=target)
'''
'''
result+=Rz((a-b)/2,target)
result+=CNOT(gate.control,target)
#result+=Rz(-(a+b)/2,target)
result+=Ry(-theta/2,target)
result+=CNOT(gate.control,target)
result+=Ry(theta/2,target)
result+=Rz(a,target)
result += Phase(numpy.pi * power / 2, gate.control)
'''
result += Rx(angle=theta, target=target, control=gate.control)
result += Phase(numpy.pi * power / 2, gate.control)
elif gate.name == 'Y':
### off by global phase of Exp[ pi power /2]
theta = power * numpy.pi
'''
result+=Phase(numpy.pi*power/2,gate.control)
result+=CNOT(gate.control,target)
result+=Ry(-theta/2,target)
result+=CNOT(gate.control,target)
result+=Ry(theta/2,target)
'''
a = 0
b = 0
# result+=Rz((a-b)/2,target)
result += CNOT(gate.control, target)
# result+=Rz(-(a+b)/2,target)
result += Ry(-theta / 2, target)
result += CNOT(gate.control, target)
result += Ry(theta / 2, target)
# result+=Rz(a,target)
result += Phase(numpy.pi * power / 2, gate.control)
elif gate.name == 'Z':
a = 0
b = power * numpy.pi
theta = 0
result += Rz(b / 2, target)
result += CNOT(gate.control, target)
result += Rz(-b / 2, target)
result += CNOT(gate.control, target)
# result+=Rz(a,target)
result += Phase(numpy.pi * power / 2, gate.control)
'''
result+=Rz(b/2,target)
result+=CNOT(gate.control,target)
result+=Rz(-b/2,target)
result+=CNOT(gate.control,target)
'''
return result
assert (numpy.isclose(wfn1.inner(wfn2), 1.0))
@pytest.mark.parametrize(
"gate, theta, phi, lambd",
[
(Rx(target=0, control=None, angle=numpy.pi / 5), numpy.pi / 5,
-numpy.pi / 2, numpy.pi / 2), # Rx(angle) = u3(angle, -pi/2, pi/2)
(Rx(target=0, control=1,
angle=numpy.pi / 6), numpy.pi / 6, -numpy.pi / 2, numpy.pi / 2),
(Rx(target=0, control=None,
angle=numpy.pi / 7), numpy.pi / 7, -numpy.pi / 2, numpy.pi / 2),
(Rx(target=0, control=1,
angle=numpy.pi / 8), numpy.pi / 8, -numpy.pi / 2, numpy.pi / 2),
(Ry(target=0, control=1, angle=numpy.pi / 4), numpy.pi / 4, 0,
0), # Ry(angle) = u3(angle, 0, 0)
(Ry(target=0, control=1, angle=numpy.pi / 5), numpy.pi / 5, 0, 0),
(Ry(target=0, control=1, angle=numpy.pi / 3), numpy.pi / 3, 0, 0),
(Ry(target=0, control=1, angle=numpy.pi / 2), numpy.pi / 2, 0, 0),
(Rz(target=0, control=None,
angle=numpy.pi), 0, 0, numpy.pi), # Rz(angle) = U(0, 0, angle)
(Rz(target=0, control=1, angle=numpy.pi / 6), 0, 0, numpy.pi / 6),
(Rz(target=0, control=None, angle=numpy.pi / 7), 0, 0, numpy.pi / 7),
(Rz(target=0, control=1, angle=numpy.pi / 8), 0, 0, numpy.pi / 8)
])
def test_unitary_gate_u_u3(gate, theta, phi, lambd):
"""
Test some equivalences for u3 gate (also U gate, because U = u3)
"""
c_u3 = u3(theta=theta,
def get_axbxc_decomp(gate):
if not isinstance(gate, PowerGateImpl) or gate.name not in ['X', 'Y', 'Z']:
return QCircuit.wrap_gate(gate)
power = gate.parameter
target = gate.target
result = QCircuit()
if gate.name == 'X':
a = -numpy.pi / 2
b = numpy.pi / 2
theta = power * numpy.pi
'''
result+=Phase(numpy.pi*power/2,gate.control)
result+=Rz(-(a-b)/2,target)
result+=CNOT(gate.control,target)
#result+=Rz(-(a+b)/2,target)
result+=Ry(-theta/2,target)
result+=CNOT(gate.control,target)
result+=Ry(theta/2,target)
result+=Rz(a,target=target)
'''
'''
result+=Rz((a-b)/2,target)
result+=CNOT(gate.control,target)
#result+=Rz(-(a+b)/2,target)
result+=Ry(-theta/2,target)
result+=CNOT(gate.control,target)
result+=Ry(theta/2,target)
result+=Rz(a,target)
result += Phase(numpy.pi * power / 2, gate.control)
'''
result += Rx(angle=theta, target=target, control=gate.control)
result += Phase(numpy.pi * power / 2, gate.control)
elif gate.name == 'Y':
### off by global phase of Exp[ pi power /2]
theta = power * numpy.pi
'''
result+=Phase(numpy.pi*power/2,gate.control)
result+=CNOT(gate.control,target)
result+=Ry(-theta/2,target)
result+=CNOT(gate.control,target)
result+=Ry(theta/2,target)
'''
a = 0
b = 0
# result+=Rz((a-b)/2,target)
result += CNOT(gate.control, target)
# result+=Rz(-(a+b)/2,target)
result += Ry(-theta / 2, target)
result += CNOT(gate.control, target)
result += Ry(theta / 2, target)
# result+=Rz(a,target)
result += Phase(numpy.pi * power / 2, gate.control)
elif gate.name == 'Z':
a = 0
b = power * numpy.pi
theta = 0
result += Rz(b / 2, target)
result += CNOT(gate.control, target)
result += Rz(-b / 2, target)
result += CNOT(gate.control, target)
# result+=Rz(a,target)
result += Phase(numpy.pi * power / 2, gate.control)
'''
result+=Rz(b/2,target)
result+=CNOT(gate.control,target)
result+=Rz(-b/2,target)
result+=CNOT(gate.control,target)
'''
return result