BF-QC: Belief Functions on Quantum Circuits

TL;DR

This paper introduces a quantum circuit-based method to efficiently implement belief functions from Dempster-Shafer Theory, reducing computational complexity and enabling advanced operations like similarity measurement and evidence combination.

Contribution

It encodes Basic Belief Assignments into quantum states and proposes new quantum algorithms to perform belief function operations more efficiently than classical methods.

Findings

Reduced computational complexity for belief function operations

Successful implementation of belief functions on quantum circuits

Enhanced methods for similarity measurement and evidence combination

Abstract

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.