BF-QC: Belief functions on quantum circuits

Dempster-Shafer Theory (DST) of belief function is a basic theory of artificial intelligence, which can represent the underlying knowledge more reasonably than Probability Theory (ProbT). Because of the computation complexity exploding exponentially with the increasing number of elements, the practical application scenarios of DST are limited. In this paper, we encode Basic Belief Assignments (BBA) into quantum superposition states and propose the implementation and operation methods of BBA on quantum circuits. We decrease the computation complexity of the Matrix Evolution on BBA (MEoB) on quantum circuits. Based on the MEoB, we realize the quantum belief functions' implementation, the similarity measurements of BBAs, evidence Combination Rules (CR), and probability transformation on quantum circuits.