def compile_phase(gate) -> QCircuit:
"""
Compile phase gates into Rz gates and cnots, if controlled
Parameters
----------
gate:
the gate
Returns
-------
QCircuit, the result of compilation.
"""
if not isinstance(gate, PhaseGateImpl):
return QCircuit.wrap_gate(gate)
phase = gate.parameter
result = QCircuit()
if len(gate.control) == 0:
return Rz(angle=phase, target=gate.target)
if len(gate.control) == 1:
result += Rz(angle=phase / 2, target=gate.control, control=None)
result += Rz(angle=phase, target=gate.target, control=gate.control)
return result
else:
return compile_controlled_phase(gate)
def compile_ry(gate: RotationGateImpl,
controlled_rotation: bool = False) -> QCircuit:
"""
Compile Ry gates into Rx and Rz.
Parameters
----------
gate:
the gate.
controlled_rotation:
determines if the decomposition of the controlled-Ry gate will be performed in compile_controlled_rotation,
if not, decomposition will be performed here
Returns
-------
QCircuit, the result of compilation.
"""
if gate.name.lower() == "ry":
if not (gate.is_controlled() and controlled_rotation):
return Rz(target=gate.target, control=None, angle=-numpy.pi / 2) \
+ Rx(target=gate.target, control=gate.control, angle=gate.parameter) \
+ Rz(target=gate.target, control=None, angle=numpy.pi / 2)
return QCircuit.wrap_gate(gate)
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 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 compile_phase(gate) -> QCircuit:
if not isinstance(gate, PhaseGateImpl):
return QCircuit.wrap_gate(gate)
phase = gate.parameter
result = QCircuit()
if len(gate.control) == 0:
return Rz(angle=phase, target=gate.target)
if len(gate.control) == 1:
result += Rz(angle=phase / 2, target=gate.control, control=None)
result += Rz(angle=phase, target=gate.target, control=gate.control)
return result
else:
return compile_controlled_phase(gate)
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 compile_controlled_phase(gate) -> QCircuit:
"""
Compile multi-controlled phase gates to 1q - phase gate and multi-controlled Rz gates.
Parameters
----------
gate:
the gate.
Returns
-------
QCircuit, the result of compilation.
"""
if not isinstance(gate, PhaseGateImpl):
return QCircuit.wrap_gate(gate)
if len(gate.control) == 0:
return QCircuit.wrap_gate(gate)
phase = gate.parameter
result = QCircuit()
result += Phase(target=gate.control[0],
control=gate.control[1:],
phi=phase / 2)
result += Rz(target=gate.target, control=gate.control, angle=phase)
return compile_controlled_phase(result)
def compile_controlled_rotation(gate: RotationGateImpl) -> QCircuit:
"""
Recompilation of a controlled-rotation gate
Basis change into Rz then recompilation of controled Rz, then change basis back
:param gate: The rotational gate
:return: set of gates wrapped in QCircuit class
"""
if not gate.is_controlled():
return QCircuit.wrap_gate(gate)
if not isinstance(gate, RotationGateImpl):
return QCircuit.wrap_gate(gate)
if len(gate.target) > 1:
return compile_controlled_rotation(gate=compile_multitarget(gate=gate))
target = gate.target
control = gate.control
k = len(control)
cind = _pattern(k) + [k - 1]
result = QCircuit()
result += change_basis(target=target, axis=gate._axis)
coeff = -1 / pow(2, k)
for i, ci in enumerate(cind):
coeff *= -1
result += Rz(target=target, angle=coeff * gate.parameter)
result += CNOT(control[ci], target)
result += change_basis(target=target, axis=gate._axis, daggered=True)
result.n_qubits = result.max_qubit() + 1
return result
def compile_controlled_power(gate: PowerGateImpl) -> QCircuit:
"""
Recompilation of a controlled-power gate
Basis change into Z then recompilation of controled Z, then change basis back
:param gate: The power gate
:return: set of gates wrapped in QCircuit class
"""
if not gate.is_controlled():
return QCircuit.wrap_gate(gate)
if not isinstance(gate, PowerGateImpl):
return QCircuit.wrap_gate(gate)
if len(gate.target) > 1:
return compile_controlled_power(gate=compile_multitarget(gate=gate))
power = gate.power
target = gate.target
control = gate.control
result = QCircuit()
result += Phase(target=control[0], control=control[1:], phi=power * pi / 2)
result += change_basis(target=target, name=gate.name)
result += Rz(target=target, control=control, angle=power * pi)
result += change_basis(target=target, name=gate.name, daggered=True)
result.n_qubits = result.max_qubit() + 1
return result
def compile_exponential_pauli_gate(gate) -> QCircuit:
"""
Returns the circuit: exp(i*angle*paulistring)
primitively compiled into X,Y Basis Changes and CNOTs and Z Rotations
:param paulistring: The paulistring in given as tuple of tuples (openfermion format)
like e.g ( (0, 'Y'), (1, 'X'), (5, 'Z') )
:param angle: The angle which parametrizes the gate -> should be real
:returns: the above mentioned circuit as abstract structure
"""
if hasattr(gate, "paulistring"):
angle = gate.paulistring.coeff * gate.parameter
circuit = QCircuit()
# the general circuit will look like:
# series which changes the basis if necessary
# series of CNOTS associated with basis changes
# Rz gate parametrized on the angle
# series of CNOT (inverted direction compared to before)
# series which changes the basis back
ubasis = QCircuit()
ubasis_t = QCircuit()
cnot_cascade = QCircuit()
last_qubit = None
previous_qubit = None
for k, v in gate.paulistring.items():
pauli = v
qubit = [k] # wrap in list for targets= ...
# see if we need to change the basis
axis = 2
if pauli.upper() == "X":
axis = 0
elif pauli.upper() == "Y":
axis = 1
ubasis += change_basis(target=qubit, axis=axis)
ubasis_t += change_basis(target=qubit, axis=axis, daggered=True)
if previous_qubit is not None:
cnot_cascade += X(target=qubit, control=previous_qubit)
previous_qubit = qubit
last_qubit = qubit
reversed_cnot = cnot_cascade.dagger()
# assemble the circuit
circuit += ubasis
circuit += cnot_cascade
circuit += Rz(target=last_qubit, angle=angle, control=gate.control)
circuit += reversed_cnot
circuit += ubasis_t
return circuit
else:
return QCircuit.wrap_gate(gate)
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_y(gate) -> QCircuit:
"""
Compile Y gates into X and Rz.
Parameters
----------
gate:
the gate.
Returns
-------
QCircuit, the result of compilation.
"""
if gate.name.lower() == "y":
return Rz(target=gate.target, control=None, angle=-numpy.pi / 2) \
+ X(target=gate.target, control=gate.control, power=gate.power if gate.is_parametrized() else None) \
+ Rz(target=gate.target, control=None, angle=numpy.pi / 2)
else:
return QCircuit.wrap_gate(gate)
def compile_controlled_phase(gate) -> QCircuit:
if not isinstance(gate, PhaseGateImpl):
return QCircuit.wrap_gate(gate)
if len(gate.control) == 0:
return QCircuit.wrap_gate(gate)
count = len(gate.control)
result = QCircuit()
phase = gate.parameter
if count == 1:
result += H(target=gate.target)
result += CNOT(gate.control, gate.target)
result += H(target=gate.target)
result += Phase(gate.parameter + numpy.pi, target=gate.target)
elif count == 2:
result += Rz(angle=phase / (2**2), target=gate.control[0])
result += Rz(angle=phase / (2**(1)),
target=gate.control[1],
control=gate.control[0])
result += Rz(angle=phase, target=gate.target, control=gate.control)
elif count >= 3:
result += Rz(angle=phase / (2**count), target=gate.control[0])
for i in range(1, count):
result += Rz(angle=phase / (2**(count - i)),
target=gate.control[i],
control=gate.control[0:i])
result += Rz(angle=phase, target=gate.target, control=gate.control)
return result
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 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 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 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
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
"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,
phi=phi,
lambd=lambd,
target=gate.gates[0].target,
control=None
if len(gate.gates[0].control) == 0 else gate.gates[0].control)