def test_total_type_jumble(simulator,value1=(numpy.random.randint(10, 1000) / 1000.0 * (numpy.pi / 2.0)),
value2=(numpy.random.randint(10, 1000) / 1000.0 * (numpy.pi / 2.0))):
a = Variable('a')
b = Variable('b')
values = {a: value1, b: value2}
H1 = tq.paulis.X(0)
H2 = tq.paulis.Y(0)
U1= tq.gates.Ry(angle=a,target=0)
U2= tq.gates.Rx(angle=b,target=0)
e1=ExpectationValue(U1,H1)
e2=ExpectationValue(U2,H2)
stacked= tq.objective.vectorize([e1, e2])
stacked = stacked*a*e2
out=simulate(stacked,variables=values,backend=simulator)
v1=out[0]
v2=out[1]
appendage = a(values) * -np.sin(b(values))
an1= np.sin(a(values)) * appendage
an2= -np.sin(b(values)) * appendage
assert np.isclose(v1+v2,an1+an2)
# not gonna contract, lets make gradient do some real work
ga=grad(stacked,a)
gb=grad(stacked,b)
la=[tq.simulate(x,variables=values) for x in ga]
print(la)
lb=[tq.simulate(x,variables=values) for x in gb]
print(lb)
tota=np.sum(np.array(la))
totb=np.sum(np.array(lb))
gan1= np.cos(a(values)) * appendage + (np.sin(a(values)) * -np.sin(b(values))) - (np.sin(b(values)) * -np.sin(b(values)))
gan2= np.sin(a(values)) * a(values) * -np.cos(b(values)) + 2 * (-np.cos(b(values)) * appendage)
assert np.isclose(tota+totb,gan1+gan2)
def test_really_awfull_thing(simulator, value1=(numpy.random.randint(10, 1000) / 1000.0 * (numpy.pi / 2.0)),
value2=(numpy.random.randint(10, 1000) / 1000.0 * (numpy.pi / 2.0))):
angle1 = Variable(name="angle1")
angle2 = Variable(name="angle2")
variables = {angle1: value1, angle2: value2}
prod = angle1 * angle2
qubit = 0
control = None
H = paulis.Y(qubit=qubit)
U = gates.Rx(target=qubit, control=control, angle=prod)
Up = gates.Rx(target=qubit, control=control, angle=prod + np.pi / 2)
Down = gates.Rx(target=qubit, control=control, angle=prod - np.pi / 2)
e1 = ExpectationValue(U=U, H=H)
en1 = simulate(e1, variables=variables, backend=simulator)
uen = simulate(0.5 * ExpectationValue(Up, H), variables=variables, backend=simulator)
den = simulate(-0.5 * ExpectationValue(Down, H), variables=variables, backend=simulator)
an1 = -np.sin(prod(variables=variables))
anval = prod(variables=variables)
an2 = angle2(variables=variables)
added = angle1 * e1
raised = added.wrap(np.sin)
dO = grad(raised, 'angle1')
dE = grad(e1, 'angle1')
dA = grad(added, 'angle1')
val = simulate(added, variables=variables, backend=simulator)
dave = simulate(dA, variables=variables, backend=simulator)
deval = simulate(dE, variables=variables, backend=simulator)
doval = simulate(dO, variables=variables, backend=simulator)
dtrue = np.cos(val) * dave
assert np.isclose(en1, an1, atol=1.e-4)
assert np.isclose(deval, an2 * (uen + den), atol=1.e-4)
assert np.isclose(doval, dtrue, atol=1.e-4)
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_akward_expression(
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}
prod = angle1 * angle2
qubit = 0
control = None
H = paulis.Y(qubit=qubit)
U = gates.Rx(target=qubit, control=control, angle=prod)
Up = gates.Rx(target=qubit, control=control, angle=prod + np.pi / 2)
Down = gates.Rx(target=qubit, control=control, angle=prod - np.pi / 2)
e1 = ExpectationValue(U=U, H=H)
en1 = simulate(e1, variables=variables, backend=simulator)
uen = simulate(0.5 * ExpectationValue(Up, H),
variables=variables,
backend=simulator)
den = simulate(-0.5 * ExpectationValue(Down, H),
variables=variables,
backend=simulator)
an1 = -np.sin(prod(variables=variables))
anval = prod(variables=variables)
an2 = angle2(variables=variables)
added = angle1 * e1
dO = grad(added, 'angle1')
dE = grad(e1, 'angle1')
deval = simulate(dE, variables=variables, backend=simulator)
doval = simulate(dO, variables=variables, backend=simulator)
dtrue = angle1(variables=variables) * deval + en1
assert np.isclose(en1, an1)
assert np.isclose(deval, an2 * (uen + den), atol=1.e-4)
assert np.isclose(doval, dtrue, atol=1.e-4)
def test_stacking():
a=Variable('a')
b=Variable('b')
def f(x):
return np.cos(x)**2. + np.sin(x)**2.
funcs=[f,f,f,f]
vals = {Variable('a'):numpy.random.uniform(0,np.pi),Variable('b'):numpy.random.uniform(0,np.pi)}
O = VectorObjective(argsets=[[a],[b],[a],[b]],transformations=funcs)
O1 = O.apply_op_list(funcs)
O2 = O1/4
output = simulate(O2,variables=vals)
assert np.isclose(1.,np.sum(output))
def test_circuit_from_moments():
c = QCircuit()
c += CNOT(target=0, control=(1, 2, 3))
c += Phase(phi=numpy.pi, target=4)
c += Rx(angle=Variable('a'), target=[0, 3])
c += H(target=[0, 1])
c += Rx(angle=Variable('a'), target=[2, 3])
## table[1] should equal 1 at this point, len(moments should be 3)
c += Z(target=1)
c += Rx(angle=Variable('a'), target=[0, 3])
moms = c.moments
c2 = QCircuit.from_moments(moms)
assert c == c2
def test_canonical_moments():
c = QCircuit()
c += CNOT(target=0, control=(1, 2, 3))
c += Rx(angle=Variable('a'), target=[0, 3])
c += H(target=[0, 1])
c += Rx(angle=Variable('a'), target=[2, 3])
c += Rx(angle=Variable('a'), target=[0, 3])
c += Z(target=1)
c += Phase(phi=numpy.pi, target=4)
moms = c.canonical_moments
assert len(moms) == 6
assert (moms[0].gates[1].parameter == assign_variable(numpy.pi))
assert (moms[0].gates[1].target == (4, ))
assert hasattr(moms[3].gates[0], 'axis')
assert len(moms[0].qubits) == 5
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_UX_HY_wfnsim(simulator, angle, controlled, silent=True):
# same as before just with wavefunction simulation
# case YX
# U = cos(angle/2) + sin(-angle/2)*i*X
# O = cos*sin*i*<0|YX|0> + sin*cos*(-i)<0|XY|0>
# = 0.5*sin(-angle)*i <0|[YX,XY]|0>
# = -sin(angle)
angle_value = angle
angle = Variable(name="angle")
variables = {angle: angle_value}
qubit = 0
H = paulis.Y(qubit=qubit)
if controlled:
control = 1
U = gates.X(target=control) + gates.Rx(
target=qubit, control=control, angle=angle)
else:
U = gates.Rx(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)
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_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 test_gradient_PHASE_HY(simulator, angle_value, controlled, silent=False):
angle = Variable(name="angle")
variables = {angle: angle_value}
qubit = 0
H = paulis.Y(qubit=qubit)
if controlled:
control = 1
U = gates.X(target=control) + gates.H(target=qubit) + gates.Phase(
target=qubit, control=control, phi=angle) + gates.H(target=qubit)
else:
U = gates.H(target=qubit) + gates.Phase(
target=qubit, phi=angle) + gates.H(target=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)
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(variables)))
print("dE =", dE)
print("-cos(angle)=", -numpy.cos(angle(variables)))
def test_conventions():
qubit = numpy.random.randint(0, 3)
angle = Variable("angle")
Rx1 = Rx(target=qubit, angle=angle)
Rx2 = QCircuit.wrap_gate(
RotationGateImpl(axis="X", target=qubit, angle=angle))
Rx3 = QCircuit.wrap_gate(
RotationGateImpl(axis="x", target=qubit, angle=angle))
Rx4 = RotationGate(axis=0, target=qubit, angle=angle)
Rx5 = RotationGate(axis="X", target=qubit, angle=angle)
Rx6 = RotationGate(axis="x", target=qubit, angle=angle)
Rx7 = RotationGate(axis=0, target=qubit, angle=angle)
Rx7.axis = "X"
ll = [Rx1, Rx2, Rx3, Rx4, Rx5, Rx6, Rx7]
for l1 in ll:
for l2 in ll:
assert (l1 == l2)
qubit = 2
for c in [None, 0, 3]:
for angle in ["angle", 0, 1.234]:
for axes in [[0, "x", "X"], [1, "y", "Y"], [2, "z", "Z"]]:
ll = [
RotationGate(axis=i, target=qubit, control=c, angle=angle)
for i in axes
]
for l1 in ll:
for l2 in ll:
assert (l1 == l2)
l1.axis = axes[numpy.random.randint(0, 2)]
assert (l1 == l2)
def test_rz_phase_flip_1(simulator, p, angle):
U = gates.X(target=0) + gates.H(1) + gates.CRz(control=0, target=1, angle=Variable('a')) + gates.H(1)
H = paulis.Z(1) * paulis.I(0)
O = ExpectationValue(U, H)
NM = PhaseFlip(p, 2)
E = simulate(O, backend=simulator, variables={'a': angle}, samples=1000, noise=NM)
print(E)
assert (numpy.isclose(E, ((1.0 - 2 * p) ** 2) * numpy.cos(angle), atol=1.e-1))
def test_gradient():
a = Variable(name='a')
variables = {a: 3.0}
b = a + 2 - 2
c = (b * 5) / 5
d = -(-c)
assert grad(d, a)(variables) == 1.0
def test_heterogeneous_operations_r(simulator, op, value1=(numpy.random.randint(1, 999) / 1000.0 * (numpy.pi / 2.0)),
value2=(numpy.random.randint(1, 999) / 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.Y(qubit=qubit)
U1 = gates.X(target=control) + gates.Rx(target=qubit, control=control, angle=angle1)
e1 = ExpectationValue(U=U1, H=H1)
added = Objective(args=[e1.args[0], angle2], transformation=op)
val = simulate(added, variables=variables, backend=simulator)
en1 = simulate(e1, variables=variables, backend=simulator)
an1 = -np.sin(angle1(variables=variables))
an2 = angle2(variables=variables)
assert np.isclose(val, float(op(en1, an2)), atol=1.e-4)
assert np.isclose(en1, an1, atol=1.e-4)
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_rz_phase_flip_0(simulator, p, angle):
qubit = 0
H = paulis.Y(qubit)
U = gates.H(target=qubit) + gates.Rz(angle=Variable('a'), target=qubit) + gates.H(target=qubit)
O = ExpectationValue(U=U, H=H)
NM = PhaseFlip(p, 1)
E = simulate(O, backend=simulator, variables={'a': angle}, samples=1000, noise=NM)
assert (numpy.isclose(E, ((-1. + 2 * p) ** 3) * numpy.sin(angle), atol=1.e-1))
def test_rx_bit_flip_0(simulator, p, angle):
U = gates.Rx(target=0, angle=Variable('a'))
H = paulis.Z(0)
NM = BitFlip(p, 1)
O = ExpectationValue(U=U, H=H)
E = simulate(O, backend=simulator, samples=1000, variables={'a': angle}, noise=NM)
assert (numpy.isclose(E, (1 - 2 * p) * numpy.cos(angle), atol=1.e-1))
def test_nesting():
a = Variable(name='a')
variables = {a: 3.0}
b = a + 2 - 2
c = (b * 5) / 5
d = -(-c)
e = d**0.5
f = e**2
assert np.isclose(a(variables), f(variables))
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 test_rx_bit_flip_0(simulator, p, angle):
U = gates.Rx(target=0, angle=Variable('a'))
H = paulis.Z(0)
NM = BitFlip(p, 1)
O = ExpectationValue(U=U, H=H)
E = simulate(O,
backend=simulator,
samples=1,
variables={'a': angle},
noise=NM)
def test_rz_phase_flip_1(simulator, p, angle):
U = gates.X(target=0) + gates.H(1) + gates.CRz(
control=0, target=1, angle=Variable('a')) + gates.H(1)
H = paulis.Z(1) * paulis.I(0)
O = ExpectationValue(U, H)
NM = PhaseFlip(p, 2)
E = simulate(O,
backend=simulator,
variables={'a': angle},
samples=1,
noise=NM)
print(E)
def test_rz_phase_flip_0(simulator, p, angle):
qubit = 0
H = paulis.Y(qubit)
U = gates.H(target=qubit) + gates.Rz(angle=Variable('a'),
target=qubit) + gates.H(target=qubit)
O = ExpectationValue(U=U, H=H)
NM = PhaseFlip(p, 1)
E = simulate(O,
backend=simulator,
variables={'a': angle},
samples=1,
noise=NM)
print(E)
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_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 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_rx_bit_flip_1(simulator, p, angle):
qubit = 1
U = gates.X(target=0) + gates.CRx(control=0, target=1, angle=Variable('a'))
H = paulis.Z(1) * paulis.I(0)
NM = BitFlip(p, 2)
O = ExpectationValue(U=U, H=H)
E = simulate(O,
backend=simulator,
samples=1,
variables={'a': angle},
noise=NM)
print(E)
print(p + numpy.cos(angle) - p * numpy.cos(angle))
def test_exotic_gradients(gradvar):
# a and b will fail for autograd not with jax
a = Variable('a')
b = Variable('b')
c = Variable('c')
d = Variable('d')
e = Variable('e')
f = Variable('f')
variables = {a: 2.0, b: 3.0, c: 4.0, d: 5.0, e: 6.0, f: 7.0}
t = c * a**b + b / c - Objective(
args=[c], transformation=np.cos) + f / (d * e) + a * Objective(
args=[d], transformation=np.exp) / (f + b) + Objective(
args=[e], transformation=np.tanh) + Objective(
args=[f], transformation=np.sinc)
g = grad(t, gradvar)
if gradvar == 'a':
assert np.isclose(
g(variables),
c(variables) * b(variables) * (a(variables)**(b(variables) - 1.)) +
np.exp(d(variables)) / (f(variables) + b(variables)))
if gradvar == 'b':
assert np.isclose(
g(variables),
(c(variables) * a(variables)**b(variables)) * np.log(a(variables))
+ 1. / c(variables) - a(variables) * np.exp(d(variables)) /
(f(variables) + b(variables))**2.0)
if gradvar == 'c':
assert np.isclose(
g(variables),
a(variables)**b(variables) - b(variables) / c(variables)**2. +
np.sin(c(variables)))
if gradvar == 'd':
assert np.isclose(
g(variables),
-f(variables) / (np.square(d(variables)) * e(variables)) +
a(variables) * np.exp(d(variables)) /
(f(variables) + b(variables)))
if gradvar == 'e':
assert np.isclose(
g(variables), 2. / (1. + np.cosh(2 * e(variables))) -
f(variables) / (d(variables) * e(variables)**2.))
if gradvar == 'f':
assert np.isclose(
g(variables), 1. / (d(variables) * e(variables)) -
a(variables) * np.exp(d(variables)) /
(f(variables) + b(variables))**2. +
np.cos(np.pi * f(variables)) / f(variables) -
np.sin(np.pi * f(variables)) / (np.pi * f(variables)**2.))
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)))
