Circuit Implementation

We start with implementing our example thus far, which was to determine the effect the Sex of a passenger and being a child (isChild) had on the Survival of the Titanic shipwreck.

A qubit represents each node in the Bayesian network. Since all our nodes in this dataset are presented as binary (Sex, isChild, Survival), a single qubit each will be sufficient. If we had more discrete states or a continuous distribution, we would need more qubits. The qubit states represent the marginal (for root nodes) and the conditional (for Survival node) probability amplitudes of the corresponding variables.

The state $|0\rangle$ represents a male passenger or an adult. The state $|1\rangle$ represents a female or a child. The superposition of the qubit denotes the probability of either state.

• $\psi_{Sex}=\sqrt{P(male)}|0\rangle+\sqrt{P(female)}|1\rangle$
• $\psi_{isChild}=\sqrt{P(adult)}|0\rangle+\sqrt{P(child)}|1\rangle$

We initialize these two qubits through rotations around the Y-axis.