  Bayesian network structure learning is an NP-hard problem that has been faced
by a number of traditional approaches in recent decades. Currently, quantum
technologies offer a wide range of advantages that can be exploited to solve
optimization tasks that cannot be addressed in an efficient way when utilizing
classic computing approaches. In this work, a specific type of variational
quantum algorithm, the quantum approximate optimization algorithm, was used to
solve the Bayesian network structure learning problem, by employing $3n(n-1)/2$
qubits, where $n$ is the number of nodes in the Bayesian network to be learned.
Our results showed that the quantum approximate optimization algorithm approach
offers competitive results with state-of-the-art methods and quantitative
resilience to quantum noise. The approach was applied to a cancer benchmark
problem, and the results justified the use of variational quantum algorithms
for solving the Bayesian network structure learning problem.
