  We propose a quantum representation of binary classification trees with
binary features based on a probabilistic approach. By using the quantum
computer as a processor for probability distributions, a probabilistic
traversal of the decision tree can be realized via measurements of a quantum
circuit. We describe how tree inductions and the prediction of class labels of
query data can be integrated into this framework. An on-demand sampling method
enables predictions with a constant number of classical memory slots,
independent of the tree depth. We experimentally study our approach using both
a quantum computing simulator and actual IBM quantum hardware. To our
knowledge, this is the first realization of a decision tree classifier on a
quantum device.
