  Dempster-Shafer Theory (DST) as an effective and robust framework for
handling uncertain information is applied in decision-making and pattern
classification. Unfortunately, its real-time application is limited by the
exponential computational complexity. People attempt to address the issue by
taking advantage of its mathematical consistency with quantum computing to
implement DST operations on quantum circuits and realize speedup. However, the
progress so far is still impractical for supporting large-scale DST
applications. In this paper, we find that Boolean algebra as an essential
mathematical tool bridges the definition of DST and quantum computing. Based on
the discovery, we establish a flexible framework mapping any set-theoretically
defined DST operations to corresponding quantum circuits for implementation.
More critically, this new framework is not only uniform but also enables
exponential acceleration for computation and is capable of handling complex
applications. Focusing on tasks of classification, we based on a classical
attribute fusion algorithm putting forward a quantum evidential classifier,
where quantum mass functions for attributes are generated with a simple method
and the proposed framework is applied for fusing the attribute evidence.
Compared to previous methods, the proposed quantum classifier exponentially
reduces the computational complexity to linear. Tests on real datasets validate
the feasibility.
