# Bayesian Network Structure Learning Using Quantum Annealing

arXiv: https://arxiv.org/abs/1407.3897 · HTML: https://mlsanity.com/paper/1407.3897/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jul 2014.

## Built on by (most cited first, 6 of 6)

- [Noisy intermediate-scale quantum (NISQ) algorithms](https://mlsanity.com/paper/2101.08448/) (2021)
- [Variational inference with a quantum computer](https://mlsanity.com/paper/2103.06720/) (2021)
- [Completely Quantum Neural Networks](https://mlsanity.com/paper/2202.11727/) (2022)
- [QUBO Decision Tree: Annealing Machine Extends Decision Tree Splitting](https://mlsanity.com/paper/2303.09772/) (2023)
- [Quantum Approximate Optimization Algorithm for Bayesian network structure learning](https://mlsanity.com/paper/2203.02400/) (2022)
- [QUBO-inspired Molecular Fingerprint for Chemical Property Prediction](https://mlsanity.com/paper/2303.10179/) (2023)

## Abstract (arXiv)

We introduce a method for the problem of learning the structure of a Bayesian network using the quantum adiabatic algorithm. We do so by introducing an efficient reformulation of a standard posterior-probability scoring function on graphs as a pseudo-Boolean function, which is equivalent to a system of 2-body Ising spins, as well as suitable penalty terms for enforcing the constraints necessary for the reformulation; our proposed method requires mathcal O(n2) qubits for n Bayesian network variables. Furthermore, we prove lower bounds on the necessary weighting of these penalty terms. The logical structure resulting from the mapping has the appealing property that it is instance-independent for a given number of Bayesian network variables, as well as being independent of the number of data cases.