Variational Quantum Linear Solver-based Combination Rules in Dempster-Shafer Theory

Dempster-Shafer Theory (DST), as a method of handling uncertain information, is widely used in decision making and information fusion. But the issue of exponential computational complexity limits its real-time application. Since quantum computers with its natural parallel computing capability can theoretically achieve speedup, an HHL-based algorithm for implementing DST operations on quantum circuits has been proposed. However, the algorithm is impossible to be implemented with high accuracy due to the limited performance of quantum computers in the current noisy intermediate-scale quantum (NISQ) era. In response to that, we utilize an up-to-date scheme Variational Quantum Linear Solver (VQLS) to conduct DST operations by solving the linear system. Besides, VQLS further reveals the structural consistency of DST with quantum computation, which enables faster circuit configuration and computation. In this paper, we first realize the transformation in belief functions by VQLS and then extends it to a methods of implementing combination rules. Simulated under a realistic classification task, the feasibility and accuracy of the proposed VQLS-based method are verified. The new VQLS-based method proposed is able to achieve combination rules at a lower error level with fewer quantum resources, which is more suitable for the NISQ era.