Quantum circuit representation of Bayesian networks

Sima E. Borujeni, Saideep Nannapaneni, Nam H. Nguyen, Elizabeth C. Behrman, James E. Steck

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 enable simulations and also has the capability to run on real quantum hardware. The results were validated against those obtained from classical Bayesian network implementations.

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