def test_application(self):
"""Test an end-to-end application."""
bounds = np.array([0., 7.])
num_qubits = 3
# the distribution circuit is a normal distribution plus a QGAN-trained ansatz circuit
dist = NormalDistribution(num_qubits, mu=1, sigma=1, bounds=bounds)
ansatz = TwoLocal(num_qubits, 'ry', 'cz', reps=1, entanglement='circular')
trained_params = [0.29399714, 0.38853322, 0.9557694, 0.07245791, 6.02626428, 0.13537225]
ansatz.assign_parameters(trained_params, inplace=True)
dist.compose(ansatz, inplace=True)
# create the European call expected value
strike_price = 2
rescaling_factor = 0.25
european_call = EuropeanCallExpectedValue(num_qubits, strike_price, rescaling_factor,
bounds)
# create the state preparation circuit
state_preparation = european_call.compose(dist, front=True)
iae = IterativeAmplitudeEstimation(0.01, 0.05, state_preparation=state_preparation,
objective_qubits=[num_qubits],
post_processing=european_call.post_processing)
backend = QuantumInstance(Aer.get_backend('qasm_simulator'),
seed_simulator=125, seed_transpiler=80)
result = iae.run(backend)
self.assertAlmostEqual(result.estimation, 1.0364776997977694)
def test_normal(self, num_qubits, mu, sigma, bounds, upto_diag):
"""Test the statevector produced by ``NormalDistribution`` and the default arguments."""
# construct default values and kwargs dictionary to call the constructor of
# NormalDistribution. The kwargs dictionary is used to not pass any arguments which are
# None to test the default values of the class.
kwargs = {'num_qubits': num_qubits, 'upto_diag': upto_diag}
if mu is None:
mu = np.zeros(len(num_qubits)) if isinstance(num_qubits,
list) else 0
else:
kwargs['mu'] = mu
if sigma is None:
sigma = np.eye(len(num_qubits)).tolist() if isinstance(
num_qubits, list) else 1
else:
kwargs['sigma'] = sigma
if bounds is None:
bounds = [
(-1, 1)
] * (len(num_qubits) if isinstance(num_qubits, list) else 1)
else:
kwargs['bounds'] = bounds
normal = NormalDistribution(**kwargs)
self.assertDistributionIsCorrect(normal, num_qubits, mu, sigma, bounds,
upto_diag)
def test_gaussian_copula_normal(self):
"""Test the Gaussian copula circuit against the normal case."""
mu = [0.1, 0.9]
sigma = [[1, -0.2], [-0.2, 1]]
num_qubits = [3, 2]
bounds = [(-1, 1), (-1, 1)]
def F(x, mean, std = 1):
return norm.cdf(x, loc = mean, scale = std)
def f(x, mean, std = 1):
return norm.pdf(x, loc = mean, scale = std)
cdfs = [lambda x:F(x, mu[0]), lambda x:F(x, mu[1])]
pdfs = [lambda x:f(x, mu[0]), lambda x:f(x, mu[1])]
normal = NormalDistribution(num_qubits, mu=mu, sigma=sigma, bounds=bounds)
gc_normal = GaussianCopula(num_qubits, cdfs, sigma=sigma, bounds=bounds, pdfs = pdfs)
sv_normal = Statevector.from_instruction(normal)
sv_gc_normal = Statevector.from_instruction(gc_normal)
np.testing.assert_array_almost_equal(sv_normal.data, sv_gc_normal.data)
def test_readme_sample(self):
"""readme sample test"""
# pylint: disable=import-outside-toplevel,redefined-builtin
def print(*args):
"""overloads print to log values"""
if args:
self.log.debug(args[0], *args[1:])
# --- Exact copy of sample code ----------------------------------------
import numpy as np
from qiskit import BasicAer
from qiskit.algorithms import AmplitudeEstimation
from qiskit.circuit.library import NormalDistribution
from qiskit_finance.applications import FixedIncomePricing
# Create a suitable multivariate distribution
num_qubits = [2, 2]
bounds = [(0, 0.12), (0, 0.24)]
mvnd = NormalDistribution(num_qubits,
mu=[0.12, 0.24],
sigma=0.01 * np.eye(2),
bounds=bounds)
# Create fixed income component
fixed_income = FixedIncomePricing(
num_qubits,
np.eye(2),
np.zeros(2),
cash_flow=[1.0, 2.0],
rescaling_factor=0.125,
bounds=bounds,
uncertainty_model=mvnd,
)
# the FixedIncomeExpectedValue provides us with the necessary rescalings
# create the A operator for amplitude estimation
problem = fixed_income.to_estimation_problem()
# Set number of evaluation qubits (samples)
num_eval_qubits = 5
# Construct and run amplitude estimation
q_i = BasicAer.get_backend("statevector_simulator")
algo = AmplitudeEstimation(num_eval_qubits=num_eval_qubits,
quantum_instance=q_i)
result = algo.estimate(problem)
print("Estimated value:\t%.4f" % fixed_income.interpret(result))
print("Probability: \t%.4f" % result.max_probability)
# ----------------------------------------------------------------------
with self.subTest("test estimation"):
self.assertAlmostEqual(result.estimation_processed, 2.46, places=4)
with self.subTest("test max.probability"):
self.assertAlmostEqual(result.max_probability, 0.8487, places=4)
def test_readme_sample(self):
""" readme sample test """
# pylint: disable=import-outside-toplevel,redefined-builtin
def print(*args):
""" overloads print to log values """
if args:
self.log.debug(args[0], *args[1:])
# --- Exact copy of sample code ----------------------------------------
import numpy as np
from qiskit import BasicAer
from qiskit.aqua.algorithms import AmplitudeEstimation
from qiskit.circuit.library import NormalDistribution
from qiskit.finance.applications import FixedIncomeExpectedValue
# Create a suitable multivariate distribution
num_qubits = [2, 2]
bounds = [(0, 0.12), (0, 0.24)]
mvnd = NormalDistribution(num_qubits,
mu=[0.12, 0.24],
sigma=0.01 * np.eye(2),
bounds=bounds)
# Create fixed income component
fixed_income = FixedIncomeExpectedValue(num_qubits,
np.eye(2),
np.zeros(2),
cash_flow=[1.0, 2.0],
rescaling_factor=0.125,
bounds=bounds)
# the FixedIncomeExpectedValue provides us with the necessary rescalings
post_processing = fixed_income.post_processing
# create the A operator for amplitude estimation by prepending the
# normal distribution to the function mapping
state_preparation = fixed_income.compose(mvnd, front=True)
# Set number of evaluation qubits (samples)
num_eval_qubits = 5
# Construct and run amplitude estimation
backend = BasicAer.get_backend('statevector_simulator')
algo = AmplitudeEstimation(num_eval_qubits,
state_preparation,
post_processing=post_processing)
result = algo.run(backend)
print('Estimated value:\t%.4f' % result.estimation)
print('Probability: \t%.4f' % result.max_probability)
# ----------------------------------------------------------------------
self.assertAlmostEqual(result.estimation, 2.46, places=4)
self.assertAlmostEqual(result.max_probability, 0.8487, places=4)
def test_application(self):
"""Test an end-to-end application."""
try:
from qiskit import Aer # pylint: disable=unused-import,import-outside-toplevel
except ImportError as ex: # pylint: disable=broad-except
self.skipTest("Aer doesn't appear to be installed. Error: '{}'".format(str(ex)))
return
bounds = np.array([0., 7.])
num_qubits = 3
# the distribution circuit is a normal distribution plus a QGAN-trained ansatz circuit
dist = NormalDistribution(num_qubits, mu=1, sigma=1, bounds=bounds)
ansatz = TwoLocal(num_qubits, 'ry', 'cz', reps=1, entanglement='circular')
trained_params = [0.29399714, 0.38853322, 0.9557694, 0.07245791, 6.02626428, 0.13537225]
ansatz.assign_parameters(trained_params, inplace=True)
dist.compose(ansatz, inplace=True)
# create the European call expected value
strike_price = 2
rescaling_factor = 0.25
european_call = EuropeanCallPricingObjective(num_state_qubits=num_qubits,
strike_price=strike_price,
rescaling_factor=rescaling_factor,
bounds=bounds)
# create the state preparation circuit
state_preparation = european_call.compose(dist, front=True)
problem = EstimationProblem(state_preparation=state_preparation,
objective_qubits=[num_qubits],
post_processing=european_call.post_processing)
q_i = QuantumInstance(Aer.get_backend('qasm_simulator'),
seed_simulator=125, seed_transpiler=80)
iae = IterativeAmplitudeEstimation(epsilon_target=0.01,
alpha=0.05,
quantum_instance=q_i)
result = iae.estimate(problem)
self.assertAlmostEqual(result.estimation_processed, 1.0127253837345427)
def test_application(self):
"""Test an end-to-end application."""
try:
from qiskit import (
Aer, ) # pylint: disable=unused-import,import-outside-toplevel
except ImportError as ex: # pylint: disable=broad-except
self.skipTest(
"Aer doesn't appear to be installed. Error: '{}'".format(
str(ex)))
return
a_n = np.eye(2)
b = np.zeros(2)
num_qubits = [2, 2]
# specify the lower and upper bounds for the different dimension
bounds = [(0, 0.12), (0, 0.24)]
mu = [0.12, 0.24]
sigma = 0.01 * np.eye(2)
# construct corresponding distribution
dist = NormalDistribution(num_qubits, mu, sigma, bounds=bounds)
# specify cash flow
c_f = [1.0, 2.0]
# specify approximation factor
rescaling_factor = 0.125
# get fixed income circuit appfactory
fixed_income = FixedIncomePricingObjective(num_qubits, a_n, b, c_f,
rescaling_factor, bounds)
# build state preparation operator
state_preparation = fixed_income.compose(dist, front=True)
problem = EstimationProblem(
state_preparation=state_preparation,
objective_qubits=[4],
post_processing=fixed_income.post_processing,
)
# run simulation
q_i = QuantumInstance(Aer.get_backend("qasm_simulator"),
seed_simulator=2,
seed_transpiler=2)
iae = IterativeAmplitudeEstimation(epsilon_target=0.01,
alpha=0.05,
quantum_instance=q_i)
result = iae.estimate(problem)
# compare to precomputed solution
self.assertAlmostEqual(result.estimation_processed, 2.3389012822103044)
def test_application(self):
"""Test an end-to-end application."""
a_n = np.eye(2)
b = np.zeros(2)
num_qubits = [2, 2]
# specify the lower and upper bounds for the different dimension
bounds = [(0, 0.12), (0, 0.24)]
mu = [0.12, 0.24]
sigma = 0.01 * np.eye(2)
# construct corresponding distribution
dist = NormalDistribution(num_qubits, mu, sigma, bounds=bounds)
# specify cash flow
c_f = [1.0, 2.0]
# specify approximation factor
rescaling_factor = 0.125
# get fixed income circuit appfactory
fixed_income = FixedIncomeExpectedValue(num_qubits, a_n, b, c_f,
rescaling_factor, bounds)
# build state preparation operator
state_preparation = fixed_income.compose(dist, front=True)
# run simulation
iae = IterativeAmplitudeEstimation(
epsilon=0.01,
alpha=0.05,
state_preparation=state_preparation,
post_processing=fixed_income.post_processing)
backend = QuantumInstance(Aer.get_backend('qasm_simulator'),
seed_simulator=2,
seed_transpiler=2)
result = iae.run(backend)
# compare to precomputed solution
self.assertAlmostEqual(result.estimation, 2.3389012822103044)
def __init__(
self,
n_normal: int,
normal_max_value: float,
p_zeros: Union[List[float], np.ndarray],
rhos: Union[List[float], np.ndarray],
) -> None:
"""
Args:
n_normal: Number of qubits to represent the latent normal random variable Z
normal_max_value: Min/max value to truncate the latent normal random variable Z
p_zeros: Standard default probabilities for each asset
rhos: Sensitivities of default probability of assets with respect to latent variable Z
"""
self.n_normal = n_normal
self.normal_max_value = normal_max_value
self.p_zeros = p_zeros
self.rhos = rhos
num_qubits = n_normal + len(p_zeros)
# get normal (inverse) CDF and pdf (these names are from the paper, therefore ignore
# pylint)
def F(x): # pylint: disable=invalid-name
return norm.cdf(x)
def F_inv(x): # pylint: disable=invalid-name
return norm.ppf(x)
def f(x): # pylint: disable=invalid-name
return norm.pdf(x)
# call super constructor
super().__init__(num_qubits, name='P(X)')
# create linear rotations for conditional defaults
slopes = []
offsets = []
for rho, p_zero in zip(rhos, p_zeros):
psi = F_inv(p_zero) / np.sqrt(1 - rho)
# compute slope / offset
slope = -np.sqrt(rho) / np.sqrt(1 - rho)
slope *= f(psi) / np.sqrt(1 - F(psi)) / np.sqrt(F(psi))
offset = 2 * np.arcsin(np.sqrt(F(psi)))
# adjust for integer to normal range mapping
offset += slope * (-normal_max_value)
slope *= 2 * normal_max_value / (2**n_normal - 1)
offsets += [offset]
slopes += [slope]
# create normal distribution
normal_distribution = NormalDistribution(n_normal,
0,
1,
bounds=(-normal_max_value,
normal_max_value))
# build circuit
self.append(normal_distribution.to_gate(), list(range(n_normal)))
for k, (slope, offset) in enumerate(zip(slopes, offsets)):
lry = LinearPauliRotations(n_normal, slope, offset)
qubits = list(range(n_normal)) + [n_normal + k]
self.append(lry.to_gate(), qubits)
def test_bounds_invalid(self, bounds):
"""Test passing invalid bounds raises."""
with self.assertRaises(ValueError):
_ = NormalDistribution([1, 1], [0, 0], [[1, 0], [0, 1]], bounds)
def test_mismatching_dimensions(self, num_qubits, mu, sigma, bounds):
"""Test passing mismatching dimensions raises an error."""
with self.assertRaises(ValueError):
_ = NormalDistribution(num_qubits, mu, sigma, bounds)
def test_distribution_load(self):
""" Test that calculates a cumulative probability from the P&L distribution."""
correl = ft.get_correl("AAPL", "MSFT")
bounds_std = 3.0
num_qubits = [3, 3]
sigma = correl
bounds = [(-bounds_std, bounds_std), (-bounds_std, bounds_std)]
mu = [0, 0]
# starting point is a multi-variate normal distribution
normal = NormalDistribution(num_qubits,
mu=mu,
sigma=sigma,
bounds=bounds)
pl_set = []
coeff_set = []
for ticker in ["MSFT", "AAPL"]:
((cdf_x, cdf_y), sigma) = ft.get_cdf_data(ticker)
(x, y) = ft.get_fit_data(ticker, norm_to_rel=False)
(pl, coeffs) = ft.fit_piecewise_linear(x, y)
# scale, to apply an arbitrary delta (we happen to use the same value here, but could be different)
coeffs = ft.scaled_coeffs(coeffs, 1.2)
pl_set.append(lambda z: ft.piecewise_linear(z, *coeffs))
coeff_set.append(coeffs)
# calculate the max and min P&Ls
p_max = max(pl_set[0](bounds_std), pl_set[1](bounds_std))
p_min = min(pl_set[0](-bounds_std), pl_set[1](-bounds_std))
# we discretise the transforms and create the circuits
transforms = []
i_to_js = []
for i, ticker in enumerate(["MSFT", "AAPL"]):
(i_0, i_1, a0, a1, a2, b0, b1, b2, i_to_j, i_to_x,
j_to_y) = ft.integer_piecewise_linear_coeffs(coeff_set[i],
x_min=-bounds_std,
x_max=bounds_std,
y_min=p_min,
y_max=p_max)
transforms.append(
PiecewiseLinearTransform3(i_0, i_1, a0, a1, a2, b0, b1, b2))
i_to_js.append(np.vectorize(i_to_j))
i1, i2 = get_sims(normal)
j1 = i_to_js[0](i1)
j2 = i_to_js[1](i2)
j_tot = j1 + j2
num_ancillas = transforms[0].num_ancilla_qubits
qr_input = QuantumRegister(6, 'input') # 2 times 3 registers
qr_objective = QuantumRegister(1, 'objective')
qr_result = QuantumRegister(6, 'result')
qr_ancilla = QuantumRegister(num_ancillas, 'ancilla')
#output = ClassicalRegister(6, 'output')
state_preparation = QuantumCircuit(qr_input, qr_objective, qr_result,
qr_ancilla) #, output)
state_preparation.append(normal, qr_input)
for i in range(2):
offset = i * 3
state_preparation.append(
transforms[i],
qr_input[offset:offset + 3] + qr_result[:] + qr_ancilla[:])
# to calculate the cdf, we use an additional comparator
x_eval = 4
comparator = IntegerComparator(len(qr_result), x_eval + 1, geq=False)
state_preparation.append(
comparator, qr_result[:] + qr_objective[:] +
qr_ancilla[0:comparator.num_ancillas])
# now check
check = False
if check:
job = execute(state_preparation,
backend=Aer.get_backend('statevector_simulator'))
var_prob = 0
for i, a in enumerate(job.result().get_statevector()):
b = ('{0:0%sb}' %
(len(qr_input) + 1)).format(i)[-(len(qr_input) + 1):]
prob = np.abs(a)**2
if prob > 1e-6 and b[0] == '1':
var_prob += prob
print('Operator CDF(%s)' % x_eval + ' = %.4f' % var_prob)
# now do AE
problem = EstimationProblem(state_preparation=state_preparation,
objective_qubits=[len(qr_input)])
# target precision and confidence level
epsilon = 0.01
alpha = 0.05
qi = QuantumInstance(Aer.get_backend('aer_simulator'), shots=100)
ae_cdf = IterativeAmplitudeEstimation(epsilon,
alpha=alpha,
quantum_instance=qi)
result_cdf = ae_cdf.estimate(problem)
conf_int = np.array(result_cdf.confidence_interval)
print('Estimated value:\t%.4f' % result_cdf.estimation)
print('Confidence interval: \t[%.4f, %.4f]' % tuple(conf_int))
state_preparation.draw()
def in_progress_test_piecewise_transform(self):
"""Simple end-to-end test of the (semi-classical) multiply and add building block."""
import numpy as np
import matplotlib.pyplot as plt
from qiskit import execute, Aer, QuantumCircuit, QuantumRegister, ClassicalRegister, AncillaRegister
from qiskit.aqua.algorithms import IterativeAmplitudeEstimation
from qiskit.circuit.library import NormalDistribution, LogNormalDistribution, LinearAmplitudeFunction, IntegerComparator, WeightedAdder
from qiskit.visualization import plot_histogram
from quantum_mc.arithmetic import multiply_add
qr_input = QuantumRegister(3, 'input')
qr_result = QuantumRegister(6, 'result')
qr_comp = QuantumRegister(2, 'comparisons')
qr_ancilla = QuantumRegister(6, 'ancilla')
qr_comp_anc = QuantumRegister(3, 'cond_ancilla')
output = ClassicalRegister(6, 'output')
circ = QuantumCircuit(qr_input, qr_result, qr_comp, qr_ancilla,
qr_comp_anc, output)
# our test piece-wise transforms:
# trans0 if x <= 2, x => 6*x + 7
# trans1 if 2 < x <= 5, x => x + 17
# trans2 if x > 5, x => 3*x + 7
sigma = 1
low = -3
high = 3
mu = 0
normal = NormalDistribution(3,
mu=mu,
sigma=sigma**2,
bounds=(low, high))
circ.append(normal, qr_input)
comp0 = IntegerComparator(num_state_qubits=3,
value=3,
name="comparator0") # true if i >= point
comp1 = IntegerComparator(num_state_qubits=3,
value=6,
name="comparator1") # true if i >= point
trans0 = multiply_add.cond_classical_add_mult(6, 7, qr_input,
qr_result, qr_ancilla)
trans1 = multiply_add.cond_classical_add_mult(1, 17, qr_input,
qr_result, qr_ancilla)
trans2 = multiply_add.cond_classical_add_mult(3, 7, qr_input,
qr_result, qr_ancilla)
circ.append(
comp0,
qr_input[:] + [qr_comp[0]] + qr_ancilla[0:comp0.num_ancillas])
circ.append(
comp1,
qr_input[:] + [qr_comp[1]] + qr_ancilla[0:comp0.num_ancillas])
# use three additional ancillas to define the ranges
circ.cx(qr_comp[0], qr_comp_anc[0])
circ.x(qr_comp_anc[0])
circ.cx(qr_comp[1], qr_comp_anc[2])
circ.x(qr_comp_anc[2])
circ.ccx(qr_comp[0], qr_comp_anc[2], qr_comp_anc[1])
circ.append(trans0, [qr_comp_anc[0]] + qr_input[:] + qr_result[:] +
qr_ancilla[:])
circ.append(trans1, [qr_comp_anc[1]] + qr_input[:] + qr_result[:] +
qr_ancilla[:])
circ.append(trans2,
[qr_comp[1]] + qr_input[:] + qr_result[:] + qr_ancilla[:])
# can uncompute qr_comp_anc
# then uncompute the comparators
circ.measure(qr_result, output)