Learning the structure of Bayesian networks is an NP-hard problem that has been tackled by several traditional methods over the last few decades. Today, quantum technologies offer a wide range of advantages that can be exploited to solve optimization tasks that cannot be handled efficiently with classical computational approaches.
In this work, a specific type of variational quantum algorithm, the approximate quantum optimization algorithm, has been used to solve the problem of learning the structure of Bayesian networks, using 3n(n - 1)/2 qubits, where n is the number of nodes in the Bayesian network to be learned.
Our results showed that the approximate quantum optimization algorithm approach offers competitive results with state-of-the-art methods and quantitative resilience to quantum noise. This approach was applied to a benchmark cancer problem, and the results justified the use of variational quantum algorithms to solve the Bayesian network structure learning problem.