def test_single_qubit_basis_transfrom():
'''
Testing whether transformations using the binary form
and the transformation through direct computation agree
'''
H, n_qubits, binary_sol, coeff_sol = prepare_test_hamiltonian()
single_qub_H, old_basis, new_basis = BinaryHamiltonian.init_from_qubit_hamiltonian(
H).single_qubit_form()
H_brute_force = brute_force_transformation(H, old_basis, new_basis)
assert (equal_qubit_hamiltonian(single_qub_H.to_qubit_hamiltonian(),
H_brute_force))
H = -1.0 * paulis.X(0) * paulis.X(1) * paulis.X(2) + 2.0 * paulis.Y(
0) * paulis.Y(1)
single_qub_H, old_basis, new_basis = BinaryHamiltonian.init_from_qubit_hamiltonian(
H).single_qubit_form()
H_brute_force = brute_force_transformation(H, old_basis, new_basis)
assert (equal_qubit_hamiltonian(single_qub_H.to_qubit_hamiltonian(),
H_brute_force))
def test_simple_arithmetic():
qubit = random.randint(0, 5)
primitives = [paulis.X, paulis.Y, paulis.Z]
assert (paulis.X(qubit).conjugate() == paulis.X(qubit))
assert (paulis.Y(qubit).conjugate() == -1 * paulis.Y(qubit))
assert (paulis.Z(qubit).conjugate() == paulis.Z(qubit))
assert (paulis.X(qubit).transpose() == paulis.X(qubit))
assert (paulis.Y(qubit).transpose() == -1 * paulis.Y(qubit))
assert (paulis.Z(qubit).transpose() == paulis.Z(qubit))
for P in primitives:
assert (P(qubit) * P(qubit) == QubitHamiltonian(1.0))
n = random.randint(0, 10)
nP = QubitHamiltonian.zero()
for i in range(n):
nP += P(qubit)
assert (n * P(qubit) == nP)
for i, Pi in enumerate(primitives):
i1 = (i + 1) % 3
i2 = (i + 2) % 3
assert (Pi(qubit) * primitives[i1](qubit) == 1j *
primitives[i2](qubit))
assert (primitives[i1](qubit) * Pi(qubit) == -1j *
primitives[i2](qubit))
for qubit2 in random.randint(6, 10, 5):
if qubit2 == qubit: continue
P = primitives[random.randint(0, 2)]
assert (Pi(qubit) * primitives[i1](qubit) * P(qubit2) == 1j *
primitives[i2](qubit) * P(qubit2))
assert (P(qubit2) * primitives[i1](qubit) * Pi(qubit) == -1j *
P(qubit2) * primitives[i2](qubit))
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 test_dagger():
assert (paulis.X(0).dagger() == paulis.X(0))
assert (paulis.Y(0).dagger() == paulis.Y(0))
assert (paulis.Z(0).dagger() == paulis.Z(0))
for repeat in range(10):
string = make_random_pauliword(complex=False)
assert (string.dagger() == string)
assert ((1j * string).dagger() == -1j * string)
def prepare_test_hamiltonian():
'''
Return a test hamiltonian and its solution
'''
H = -1.0 * paulis.Z(0) * paulis.Z(1) - 0.5 * paulis.Y(0) * paulis.Y(
1) + 0.1 * paulis.X(0) * paulis.X(1) + 0.2 * paulis.Z(2)
coeff_sol = np.array([-1.0, -0.5, 0.1, 0.2])
binary_sol = np.array([[0, 0, 0, 1, 1, 0], [1, 1, 0, 1, 1, 0],
[1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1]])
return H, H.n_qubits, binary_sol, coeff_sol
def test_matrix_form():
H = -1.0 * paulis.Z(0) -1.0 * paulis.Z(1) + 0.1 * paulis.X(0)*paulis.X(1)
Hm= H.to_matrix()
assert (Hm[0,0] == -2.0)
assert (Hm[0,3] == 0.10)
assert (Hm[1,2] == 0.10)
Hm2 = (H + paulis.Z(2)).to_matrix()
Hm2p = kron(Hm, eye(2, dtype=Hm2.dtype)) + kron(eye(len(Hm), dtype=Hm2.dtype), paulis.Z(0).to_matrix())
assert allclose(Hm2 , Hm2p)
Hm3 = (H * paulis.Z(2)).to_matrix()
Hm3p = kron(Hm, paulis.Z(0).to_matrix())
assert allclose(Hm3 , Hm3p)
def assign_generator(axis, qubits):
if axis == 0:
return sum(paulis.X(q) for q in qubits)
if axis == 1:
return sum(paulis.Y(q) for q in qubits)
return sum(paulis.Z(q) for q in qubits)
def test_gradient_deep_H(simulator, power, controls):
if controls > 2 and simulator == "qiskit":
# does not work yet
return
qubit = 0
angle = Variable(name="angle")
variables = {angle: power}
control = [i for i in range(1, controls + 1)]
H = paulis.X(qubit=qubit)
U = gates.X(target=control) + gates.H(
target=qubit, control=control, power=angle)
O = ExpectationValue(U=U, H=H)
E = simulate(O, variables=variables, backend=simulator)
assert (numpy.isclose(E,
-numpy.cos(angle(variables) * (numpy.pi)) / 2 + 0.5,
atol=1.e-4))
dO = grad(objective=O, variable=angle)
dE = simulate(dO, variables=variables, backend=simulator)
assert (numpy.isclose(dE,
numpy.pi * numpy.sin(angle(variables) * (numpy.pi)) /
2,
atol=1.e-4))
def test_gradient_H(simulator, power, controlled):
qubit = 0
control = 1
angle = Variable(name="angle")
variables = {angle: power}
H = paulis.X(qubit=qubit)
if not controlled:
U = gates.H(target=qubit, power=angle)
else:
U = gates.X(target=control) + gates.H(
target=qubit, control=control, power=angle)
O = ExpectationValue(U=U, H=H)
E = simulate(O, variables=variables, backend=simulator)
assert (numpy.isclose(E,
-numpy.cos(angle(variables) * (numpy.pi)) / 2 + 0.5,
atol=1.e-4))
dO = grad(objective=O, variable=angle)
dE = simulate(dO, variables=variables, backend=simulator)
assert (numpy.isclose(dE,
numpy.pi * numpy.sin(angle(variables) * (numpy.pi)) /
2,
atol=1.e-4))
def test_gradient_UY_HX(simulator, angle_value, controlled, silent=True):
# case X Y
# U = cos(angle/2) + sin(-angle/2)*i*Y
# <0|Ud H U |0> = cos^2(angle/2)*<0|X|0>
# + sin^2(-angle/2) <0|YXY|0>
# + cos(angle/2)*sin(angle/2)*i<0|XY|0>
# + sin(-angle/2)*cos(angle/2)*(-i) <0|YX|0>
# = cos^2*0 + sin^2*0 + cos*sin*i(<0|[XY,YX]|0>)
# = 0.5*sin(-angle)*i <0|[XY,YX]|0> = -0.5*sin(angle)*i * 2 i <0|Z|0>
# = sin(angle)
angle = Variable(name="angle")
variables = {angle: angle_value}
qubit = 0
H = paulis.X(qubit=qubit)
if controlled:
control = 1
U = gates.X(target=control) + gates.Ry(
target=qubit, control=control, angle=angle)
else:
U = gates.X(target=qubit) + gates.X(target=qubit) + gates.Ry(
target=qubit, angle=angle)
O = ExpectationValue(U=U, H=H)
E = simulate(O, variables=variables, backend=simulator)
print("O={type}".format(type=type(O)))
dO = grad(objective=O, variable=angle)
dE = simulate(dO, variables=variables, backend=simulator)
assert (numpy.isclose(E, numpy.sin(angle(variables)), atol=1.e-4))
assert (numpy.isclose(dE, numpy.cos(angle(variables)), atol=1.e-4))
if not silent:
print("E =", E)
print("sin(angle)=", numpy.sin(angle()))
print("dE =", dE)
print("cos(angle)=", numpy.cos(angle()))
def get_generator(gate) -> paulis.QubitHamiltonian:
"""
get the generator of a gaussian gate as a Qubit hamiltonian. Relies on the name of the gate.
Parameters
----------
gate: QGateImpl:
QGateImpl object or inheritor thereof, with name corresponding to its generator in some fashion.
Returns
-------
QubitHamiltonian:
the generator of the gate acting, on the gate's target.
"""
if gate.name.lower() == 'rx':
gen = paulis.X(gate.target[0])
elif gate.name.lower() == 'ry':
gen = paulis.Y(gate.target[0])
elif gate.name.lower() == 'rz':
gen = paulis.Z(gate.target[0])
elif gate.name.lower() == 'phase':
gen = paulis.Qm(gate.target[0])
else:
print(gate.name.lower())
raise TequilaException(
'cant get the generator of a non Gaussian gate, you fool!')
return gen
def test_mixed_power(
simulator,
value1=(numpy.random.randint(0, 1000) / 1000.0 * (numpy.pi / 2.0)),
value2=(numpy.random.randint(0, 1000) / 1000.0 * (numpy.pi / 2.0))):
angle1 = Variable(name="angle1")
angle2 = Variable(name="angle2")
variables = {angle1: value1, angle2: value2}
qubit = 0
control = 1
H1 = paulis.X(qubit=qubit)
U1 = gates.X(target=control) + gates.Ry(
target=qubit, control=control, angle=angle1)
e1 = ExpectationValue(U=U1, H=H1)
H2 = paulis.Y(qubit=qubit)
U2 = gates.X(target=control) + gates.Rx(
target=qubit, control=control, angle=angle2)
e2 = ExpectationValue(U=U2, H=H2)
added = e1**e2
val = simulate(added, variables=variables, backend=simulator)
en1 = simulate(e1, variables=variables, backend=simulator)
en2 = simulate(e2, variables=variables, backend=simulator)
an1 = np.sin(angle1(variables=variables))
an2 = -np.sin(angle2(variables=variables))
assert np.isclose(val, en1**en2, atol=1.e-4)
assert np.isclose(val, an1**an2, atol=1.e-4)
def test_hadamard(qubit, init):
gate = gates.H(target=qubit)
iwfn = QubitWaveFunction.from_int(i=init, n_qubits=qubit + 1)
wfn = simulate(gate, initial_state=init)
test = 1.0 / numpy.sqrt(2) * (iwfn.apply_qubitoperator(paulis.Z(qubit)) +
iwfn.apply_qubitoperator(paulis.X(qubit)))
assert (wfn.isclose(test))
def test_phase_damp(simulator, p):
qubit = 0
H = paulis.X(qubit)
U = gates.H(target=qubit)
O = ExpectationValue(U=U, H=H)
NM = PhaseDamp(p, 1)
E = simulate(O, backend=simulator, samples=1, noise=NM)
def test_phase_flip(simulator, p):
qubit = 0
H = paulis.X(qubit)
U = gates.H(target=qubit)
O = ExpectationValue(U=U, H=H)
NM = PhaseFlip(p, 1)
E = simulate(O, backend=simulator, samples=1000, noise=NM)
assert (numpy.isclose(E, 1.0 - 2 * p, atol=1.e-1))
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_commuting_groups():
'''
Testing whether the partitioning gives commuting parts
'''
H, _, _, _ = prepare_test_hamiltonian()
H = H + paulis.X(0) + paulis.Y(0)
H = BinaryHamiltonian.init_from_qubit_hamiltonian(H)
commuting_parts = H.commuting_groups()
for part in commuting_parts:
assert part.is_commuting()
def test_compilation(backend):
U = gates.X(target=[0, 1, 2, 3, 4, 5])
for i in range(10):
U += gates.Ry(angle=(i, ), target=numpy.random.randint(0, 5, 1)[0])
U += gates.CZ(0, 1) + gates.CNOT(1, 2) + gates.CZ(2, 3) + gates.CNOT(
3, 4) + gates.CZ(5, 6)
H = paulis.X(0) + paulis.X(1) + paulis.X(2) + paulis.X(3) + paulis.X(
4) + paulis.X(5)
H += paulis.Z(0) + paulis.Z(1) + paulis.Z(2) + paulis.Z(3) + paulis.Z(
4) + paulis.Z(5)
E = ExpectationValue(H=H, U=U)
randvals = numpy.random.uniform(0.0, 2.0, 10)
variables = {(i, ): randvals[i] for i in range(10)}
e0 = simulate(E, variables=variables, backend=backend)
E2 = E * E
for i in range(99):
E2 += E * E
compiled = tq.compile(E2, variables=variables, backend=backend)
e2 = compiled(variables=variables)
assert (E2.count_expectationvalues(unique=True) == 1)
assert (compiled.count_expectationvalues(unique=True) == 1)
assert numpy.isclose(100 * e0**2, e2)
def test_l_division(simulator, value=numpy.random.uniform(0.0, 2.0*numpy.pi, 1)[0]):
angle1 = Variable(name="angle1")
variables = {angle1: value}
qubit = 0
control = 1
H1 = paulis.X(qubit=qubit)
U1 = gates.X(target=control) + gates.Ry(target=qubit, control=control, angle=angle1)
e1 = ExpectationValue(U=U1, H=H1)
added = e1 / 2
val = simulate(added, variables=variables, backend=simulator)
en1 = simulate(e1, variables=variables, backend=simulator) / 2
an1 = np.sin(value) / 2.
assert np.isclose(val, en1, atol=1.e-4)
assert np.isclose(val, an1, atol=1.e-4)
def get_generator(gate):
if gate.name.lower() == 'rx':
gen = paulis.X(gate.target[0])
elif gate.name.lower() == 'ry':
gen = paulis.Y(gate.target[0])
elif gate.name.lower() == 'rz':
gen = paulis.Z(gate.target[0])
elif gate.name.lower() == 'phase':
gen = paulis.Qm(gate.target[0])
else:
print(gate.name.lower())
raise TequilaException(
'cant get the generator of a non Gaussian gate, you fool!')
return gen
def test_r_power(simulator, value=numpy.random.uniform(0.1, 1.9*numpy.pi, 1)[0]):
angle1 = Variable(name="angle1")
variables = {angle1: value}
qubit = 0
control = 1
H1 = paulis.X(qubit=qubit)
U1 = gates.X(target=control) + gates.Ry(target=qubit, control=control, angle=angle1)
e1 = ExpectationValue(U=U1, H=H1)
added = 2 ** e1
val = simulate(added, variables=variables, backend=simulator)
en1 = 2 ** simulate(e1, variables=variables, backend=simulator)
an1 = 2. ** np.sin(angle1(variables=variables))
assert np.isclose(val, en1, atol=1.e-4)
assert np.isclose(val, an1, atol=1.e-4)
def test_l_addition(simulator, value=(numpy.random.randint(0, 1000) / 1000.0 * (numpy.pi / 2.0))):
angle1 = Variable(name="angle1")
variables = {angle1: value}
qubit = 0
control = 1
H1 = paulis.X(qubit=qubit)
U1 = gates.X(target=control) + gates.Ry(target=qubit, control=control, angle=angle1)
e1 = ExpectationValue(U=U1, H=H1)
added = e1 + 1
val = simulate(added, variables=variables, backend=simulator)
en1 = simulate(e1, variables=variables, backend=simulator) + 1.
an1 = np.sin(angle1(variables=variables)) + 1.
assert np.isclose(val, en1, atol=1.e-4)
assert np.isclose(val, an1, atol=1.e-4)
def test_special_operators():
# sigma+ sigma- as well as Q+ and Q-
assert (paulis.Sp(0) * paulis.Sp(0) == QubitHamiltonian.zero())
assert (paulis.Sm(0) * paulis.Sm(0) == QubitHamiltonian.zero())
assert (paulis.Qp(0) * paulis.Qp(0) == paulis.Qp(0))
assert (paulis.Qm(0) * paulis.Qm(0) == paulis.Qm(0))
assert (paulis.Qp(0) * paulis.Qm(0) == QubitHamiltonian.zero())
assert (paulis.Qm(0) * paulis.Qp(0) == QubitHamiltonian.zero())
assert (paulis.Sp(0) * paulis.Sm(0) == paulis.Qp(0))
assert (paulis.Sm(0) * paulis.Sp(0) == paulis.Qm(0))
assert (paulis.Sp(0) + paulis.Sm(0) == paulis.X(0))
assert (paulis.Qp(0) + paulis.Qm(0) == paulis.I(0))
def test_heterogeneous_operations_l(simulator, op, value1=(numpy.random.randint(1, 1000) / 1000.0 * (numpy.pi / 2.0)),
value2=(numpy.random.randint(1, 1000) / 1000.0 * (numpy.pi / 2.0))):
angle1 = Variable(name="angle1")
angle2 = Variable(name="angle2")
variables = {angle1: value1, angle2: value2}
qubit = 0
control = 1
H2 = paulis.X(qubit=qubit)
U2 = gates.X(target=control) + gates.Ry(target=qubit, control=control, angle=angle2)
e2 = ExpectationValue(U=U2, H=H2)
added = Objective(args=[angle1, e2.args[0]], transformation=op)
val = simulate(added, variables=variables, backend=simulator)
en2 = simulate(e2, variables=variables, backend=simulator)
an1 = angle1(variables=variables)
an2 = np.sin(angle2(variables=variables))
assert np.isclose(val, float(op(an1, en2)), atol=1.e-4)
assert np.isclose(en2, an2, atol=1.e-4)
def test_gradient_Y(simulator, power, controlled):
if simulator != "cirq":
return
qubit = 0
control = 1
angle = Variable(name="angle")
if controlled:
U = gates.X(target=control) + gates.Y(target=qubit, power=angle, control=control)
else:
U = gates.Y(target=qubit, power=angle)
angle = Variable(name="angle")
variables = {angle: power}
H = paulis.X(qubit=qubit)
O = ExpectationValue(U=U, H=H)
E = simulate(O, variables=variables, backend=simulator)
dO = grad(objective=O, variable=angle)
dE = simulate(dO, variables=variables, backend=simulator)
assert (numpy.isclose(E, numpy.sin(angle(variables) * (numpy.pi)), atol=1.e-4))
assert (numpy.isclose(dE, numpy.pi * numpy.cos(angle(variables) * (numpy.pi)), atol=1.e-4))
def H(target: typing.Union[list, int],
control: typing.Union[list, int] = None,
power=None,
angle=None,
*args,
**kwargs) -> QCircuit:
"""
Notes
----------
Hadamard gate
Parameters
----------
target
int or list of int
control
int or list of int
power
numeric type (fixed exponent) or hashable type (parametrized exponent)
angle
similar to power, but will be interpreted as
.. math::
U(\\text{angle})=e^{-i\\frac{angle}{2} generator}
the default is angle=pi
.. math::
U(\\pi) = H
If angle and power are given both, tequila will combine them
Returns
-------
QCircuit object
"""
coef = 1 / np.sqrt(2)
generator = lambda q: coef * (paulis.Z(q) + paulis.X(q)) - paulis.I(q)
return _initialize_power_gate(name="H",
power=power,
angle=angle,
target=target,
control=control,
generator=generator,
*args,
**kwargs)
def SWAP(first: int,
second: int,
control: typing.Union[int, list] = None,
power: float = None,
*args,
**kwargs) -> QCircuit:
"""
Notes
----------
SWAP gate, order of targets does not matter
Parameters
----------
first: int
target qubit
second: int
target qubit
control
int or list of ints
power
numeric type (fixed exponent) or hashable type (parametrized exponent)
Returns
-------
QCircuit
"""
target = [first, second]
generator = 0.5 * (paulis.X(target) + paulis.Y(target) + paulis.Z(target) -
paulis.I(target))
if power is None or power in [1, 1.0]:
return QGate(name="SWAP",
target=target,
control=control,
generator=generator)
else:
return GeneralizedRotation(angle=power * np.pi,
control=control,
generator=generator,
eigenvalues_magnitude=0.25)
def test_gradient_UY_HX_wfnsim(simulator,
angle_value,
controlled,
silent=True):
# same as before just with wavefunction simulation
# case X Y
# U = cos(angle/2) + sin(-angle/2)*i*Y
# <0|Ud H U |0> = cos^2(angle/2)*<0|X|0>
# + sin^2(-angle/2) <0|YXY|0>
# + cos(angle/2)*sin(angle/2)*i<0|XY|0>
# + sin(-angle/2)*cos(angle/2)*(-i) <0|YX|0>
# = cos^2*0 + sin^2*0 + cos*sin*i(<0|[XY,YX]|0>)
# = 0.5*sin(-angle)*i <0|[XY,YX]|0> = -0.5*sin(angle)*i * 2 i <0|Z|0>
# = sin(angle)
angle = Variable(name="angle")
variables = {angle: angle_value}
qubit = 0
H = paulis.X(qubit=qubit)
if controlled:
control = 1
U = gates.X(target=control) + gates.Ry(
target=qubit, control=control, angle=angle)
else:
U = gates.Ry(target=qubit, angle=angle)
O = ExpectationValue(U=U, H=H)
E = simulate(O, variables=variables, backend=simulator)
dO = grad(objective=O, variable='angle')
dE = simulate(dO, variables=variables, backend=simulator)
E = numpy.float(E) # for isclose
dE = numpy.float(dE) # for isclose
assert (numpy.isclose(E, numpy.sin(angle(variables)), atol=0.0001))
assert (numpy.isclose(dE, numpy.cos(angle(variables)), atol=0.0001))
if not silent:
print("E =", E)
print("sin(angle)=", numpy.sin(angle(variables)))
print("dE =", dE)
print("cos(angle)=", numpy.cos(angle(variables)))
def test_transposition():
primitives = [paulis.X, paulis.Y, paulis.Z]
factors = [1, -1, 1j, -1j, 0.5 + 1j]
assert ((paulis.X(0) * paulis.X(1) * paulis.Y(2)).transpose() == -1 *
paulis.X(0) * paulis.X(1) * paulis.Y(2))
assert ((paulis.X(0) * paulis.X(1) *
paulis.Z(2)).transpose() == paulis.X(0) * paulis.X(1) *
paulis.Z(2))
for repeat in range(10):
string = QubitHamiltonian.unit()
tstring = QubitHamiltonian.unit()
for q in range(5):
ri = random.randint(0, 2)
P = primitives[ri]
sign = 1
if ri == 1:
sign = -1
factor = factors[random.randint(0, len(factors) - 1)]
string *= factor * P(qubit=q)
tstring *= factor * sign * P(qubit=q)
assert (string.transpose() == tstring)
def X(target: typing.Union[list, int],
control: typing.Union[list, int] = None,
power=None,
angle=None) -> QCircuit:
"""
Notes
----------
Pauli X Gate
Parameters
----------
target
int or list of int
control
int or list of int
power
numeric type (fixed exponent) or hashable type (parametrized exponent)
angle
similar to power, but will be interpreted as
.. math::
U(\\text{angle})=e^{-i\\frac{angle}{2} (1-X)}
the default is angle=pi
.. math::
U(\\pi) = X
If angle and power are given both, tequila will combine them
Returns
-------
QCircuit object
"""
generator = lambda q: paulis.X(q) - paulis.I(q)
return _initialize_power_gate(name="X",
power=power,
angle=angle,
target=target,
control=control,
generator=generator)