  Probabilistic graphical models such as Bayesian networks are widely used to
model stochastic systems to perform various types of analysis such as
probabilistic prediction, risk analysis, and system health monitoring, which
can become computationally expensive in large-scale systems. While
demonstrations of true quantum supremacy remain rare, quantum computing
applications managing to exploit the advantages of amplitude amplification have
shown significant computational benefits when compared against their classical
counterparts. We develop a systematic method for designing a quantum circuit to
represent a generic discrete Bayesian network with nodes that may have two or
more states, where nodes with more than two states are mapped to multiple
qubits. The marginal probabilities associated with root nodes (nodes without
any parent nodes) are represented using rotation gates, and the conditional
probability tables associated with non-root nodes are represented using
controlled rotation gates. The controlled rotation gates with more than one
control qubit are represented using ancilla qubits. The proposed approach is
demonstrated for three examples: a 4-node oil company stock prediction, a
10-node network for liquidity risk assessment, and a 9-node naive Bayes
classifier for bankruptcy prediction. The circuits were designed and simulated
using Qiskit, a quantum computing platform that enables simulations and also
has the capability to run on real quantum hardware. The results were validated
against those obtained from classical Bayesian network implementations.

Quantum Physics;Computational Engineering, Finance, and Science