Quantum algorithm of Dempster rule of combination

Abstract

Dempster rule of combination is a powerful combination tool. It has been widely used in many fields, such as information fusion and decision-making. However, the computational complexity of Dempster rule of combination increases exponentially with the increase of frame of discernment. To address this issue, leveraging the parallel advantage of quantum computing, we present a quantum algorithm of Dempster rule of combination. The new method includes four steps. First, the quantum superposition states corresponding to arbitrary mass functions are prepared. Next, the superposition states corresponding to the two mass functions are combined by the tensor product. Effective qubits are then measured. Finally, the measurement results are normalized to obtain the combined results. The new method not only realizes most of the functions of Dempster rule of combination, but also effectively reduces the computational complexity of Dempster rule of combination in the quantum computer. Finally, we carry out the simulation experiments on the quantum cloud platform of IBM, and the experimental results show that the new method is reasonable. Compared with the traditional combination rule, this method effectively reduces the computational complexity. As the frame of discernment becomes larger, the advantages of the proposed approach in terms of running time become larger and larger.