def test_trace_out_xy(theta):
a = numpy.sin(theta)
b = numpy.cos(theta)
state = QubitWaveFunction.from_array([a,b])
H1 = QubitHamiltonian.from_string("1.0*X(0)*X(1)*X(100)")
H2 = QubitHamiltonian.from_string("1.0*X(0)*X(100)")
factor = a.conjugate()*b + b.conjugate()*a
assert factor*H2 == H1.trace_out_qubits(qubits=[1,3,5], states=[state]*3)
factor *= factor
H1 = QubitHamiltonian.from_string("1.0*X(0)*X(1)*X(5)*X(100)")
assert factor*H2 == H1.trace_out_qubits(qubits=[1,3,5], states=[state]*3)
H1 = QubitHamiltonian.from_string("1.0*X(0)*Y(1)*X(100)")
H2 = QubitHamiltonian.from_string("1.0*X(0)*X(100)")
factor = -1.0j*(a.conjugate()*b - b.conjugate()*a)
assert factor*H2 == H1.trace_out_qubits(qubits=[1,3,5], states=[state]*3)
factor *= factor
H1 = QubitHamiltonian.from_string("1.0*X(0)*Y(1)*Y(5)*X(100)")
assert factor*H2 == H1.trace_out_qubits(qubits=[1,3,5], states=[state]*3)
H1 = QubitHamiltonian.from_string("1.0*X(0)*X(1)*X(100)")
H2 = QubitHamiltonian.from_string("1.0*X(0)*X(100)")
factor = a.conjugate()*b + b.conjugate()*a
assert factor*H2 == H1.trace_out_qubits(qubits=[1,3,5], states=[state]*3)
factor *= -1.0j*(a.conjugate()*b - b.conjugate()*a)
H1 = QubitHamiltonian.from_string("1.0*X(0)*X(1)*Y(5)*X(100)")
assert factor*H2 == H1.trace_out_qubits(qubits=[1,3,5], states=[state]*3)
def test_initialization():
H = paulis.I()
for i in range(10):
H += paulis.pauli(qubit=numpy.random.randint(0,5,3), type=numpy.random.choice(["X", "Y", "Z"],1))
for H1 in [H, paulis.I(), paulis.Zero(), paulis.X(0), paulis.Y(1), 1.234*paulis.Z(2)]:
string = str(H1)
ofstring = str(H1.to_openfermion())
H2 = QubitHamiltonian.from_string(string=string)
assert H1 == H2
H3 = QubitHamiltonian.from_string(string=ofstring, openfermion_format=True)
assert H1 == H3
def test_paulistring_conversion():
X1 = QubitHamiltonian.from_string("X0", openfermion_format=True)
X2 = paulis.X(0)
keys = [i for i in X2.keys()]
pwx = PauliString.from_openfermion(key=keys[0], coeff=X2[keys[0]])
X3 = QubitHamiltonian.from_paulistrings(pwx)
assert (X1 == X2)
assert (X2 == X3)
H = paulis.X(0) * paulis.Y(1) * paulis.Z(2) + paulis.X(3) * paulis.Y(
4) * paulis.Z(5)
PS = []
for key, value in H.items():
PS.append(PauliString.from_openfermion(key, value))
PS2 = H.paulistrings
assert (PS == PS2)
H = make_random_pauliword(complex=True)
for i in range(5):
H += make_random_pauliword(complex=True)
PS = []
for key, value in H.items():
PS.append(PauliString.from_openfermion(key, value))
PS2 = H.paulistrings
assert (PS == PS2)
def pauli(qubit, type) -> QubitHamiltonian:
"""
Parameters
----------
qubit: int or list of ints
type: str or int or list of string or int:
define if X, Y or Z (0,1,2)
Returns
-------
QubitHamiltonian
"""
def assign_axis(axis):
if axis in QubitHamiltonian.axis_to_string:
return QubitHamiltonian.axis_to_string[axis]
elif hasattr(axis, "upper"):
return axis.upper()
else:
raise TequilaException(
"unknown initialization for pauli operator: {}".format(axis))
if not isinstance(qubit, typing.Iterable):
qubit = [qubit]
type = [type]
type = [assign_axis(x) for x in type]
init_string = "".join("{}{} ".format(t, q) for t, q in zip(type, qubit))
return QubitHamiltonian.from_string(string=init_string,
openfermion_format=True)
def test_convenience():
i = numpy.random.randint(0, 10, 1)[0]
assert paulis.X(i) + paulis.I(i) == paulis.X(i) + 1.0
assert paulis.Qp(i) == 0.5 * (1.0 + paulis.Z(i))
assert paulis.Qm(i) == 0.5 * (1.0 - paulis.Z(i))
assert paulis.Sp(i) == 0.5 * (paulis.X(i) + 1.j * paulis.Y(i))
assert paulis.Sm(i) == 0.5 * (paulis.X(i) - 1.j * paulis.Y(i))
i = numpy.random.randint(0, 10, 1)[0]
assert paulis.Qp(i) == (0.5 + 0.5 * paulis.Z(i))
assert paulis.Qm(i) == (0.5 - 0.5 * paulis.Z(i))
assert paulis.Sp(i) == (0.5 * paulis.X(i) + 0.5j * paulis.Y(i))
assert paulis.Sm(i) == (0.5 * paulis.X(i) - 0.5j * paulis.Y(i))
assert -1.0 * paulis.Y(i) == -paulis.Y(i)
test = paulis.Z(i)
test *= -1.0
assert test == -paulis.Z(i)
test = paulis.Z(i)
test += 1.0
assert test == paulis.Z(i) + 1.0
test = paulis.X(i)
test += paulis.Y(i + 1)
assert test == paulis.X(i) + paulis.Y(i + 1)
test = paulis.X(i)
test -= paulis.Y(i)
test += 3.0
test = -test
assert test == -1.0 * (paulis.X(i) - paulis.Y(i) + 3.0)
test = paulis.X([0, 1, 2, 3])
assert test == QubitHamiltonian.from_string("X(0)X(1)X(2)X(3)", False)
test = paulis.Y([0, 1, 2, 3])
assert test == QubitHamiltonian.from_string("Y(0)Y(1)Y(2)Y(3)", False)
test = paulis.Z([0, 1, 2, 3])
assert test == QubitHamiltonian.from_string("Z(0)Z(1)Z(2)Z(3)", False)
def __init__(self,
name,
generator: QubitHamiltonian,
target: list,
power,
control: list = None):
if generator is None:
assert name is not None and name.upper() in ["X", "Y", "Z"]
generator = QubitHamiltonian.from_string("{}({})".format(
name.upper(), target))
if name is None:
assert generator is not None
name = str(generator)
super().__init__(name=name,
parameter=power * pi,
target=target,
control=control,
generator=generator)
def test_simple_trace_out():
H1 = QubitHamiltonian.from_string("1.0*Z(0)*Z(1)")
H2 = QubitHamiltonian.from_string("1.0*Z(0)")
assert H2 == H1.trace_out_qubits(qubits=[1], states=None)
H1 = QubitHamiltonian.from_string("1.0*Z(0)*Z(1)X(100)")
H2 = QubitHamiltonian.from_string("1.0*Z(1)X(100)")
assert H2 == H1.trace_out_qubits(qubits=[0], states=None)
H1 = QubitHamiltonian.from_string("1.0*Z(0)*Z(1)X(100)")
H2 = QubitHamiltonian.from_string("-1.0*Z(0)X(100)")
assert H2 == H1.trace_out_qubits(qubits=[1], states=[QubitWaveFunction.from_string("1.0*|1>")])
H1 = QubitHamiltonian.from_string("1.0*Z(0)*Z(1)X(100)")
H2 = QubitHamiltonian.from_string("-1.0*Z(1)X(100)")
assert H2 == H1.trace_out_qubits(qubits=[0], states=[QubitWaveFunction.from_string("1.0*|1>")])
H1 = QubitHamiltonian.from_string("1.0*X(0)*Z(1)*Z(5)*X(100)Y(50)")
H2 = QubitHamiltonian.from_string("1.0*X(0)X(100)Y(50)")
assert H2 == H1.trace_out_qubits(qubits=[1,5], states=[QubitWaveFunction.from_string("1.0*|1>")]*2)
H1 = QubitHamiltonian.from_string("1.0*X(0)*Z(1)*X(100)Y(50)")
H2 = QubitHamiltonian.from_string("-1.0*X(0)X(100)Y(50)")
assert H2 == H1.trace_out_qubits(qubits=[1,5], states=[QubitWaveFunction.from_string("1.0*|1>")]*2)