Source code for qiskit_finance.circuit.library.probability_distributions.gaussian_conditional_independence_model

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# (C) Copyright IBM 2019, 2023.
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"""The Gaussian Conditional Independence Model for Credit Risk."""

from typing import List, Union
import numpy as np
from scipy.stats.distributions import norm

from qiskit.circuit import QuantumCircuit
from qiskit.circuit.library import LinearPauliRotations
from .normal import NormalDistribution

[docs]class GaussianConditionalIndependenceModel(QuantumCircuit): """The Gaussian Conditional Independence Model for Credit Risk. Reference: Dependency between individual risk variables and latent variable is approximated linearly. """ 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) # 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 inner = QuantumCircuit(num_qubits, name="P(X)") inner.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] inner.append(lry.to_gate(), qubits) super().__init__(num_qubits, name="P(X)") self.append(inner.to_gate(), inner.qubits)