# BF-QC: Belief Functions on Quantum Circuits

arXiv: https://arxiv.org/abs/2107.03930 · HTML: https://mlsanity.com/paper/2107.03930/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 81 references that are in the map.
- First posted on arXiv 8 Jul 2021.

## Builds on (most cited first, 5 of 5)

- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [Quantum Inference on Bayesian Networks](https://mlsanity.com/paper/1402.7359/) (2014)
- [Logistic Regression, Neural Networks and Dempster-Shafer Theory: a New Perspective](https://mlsanity.com/paper/1807.01846/) (2018)
- [Expert Opinion Extraction from a Biomedical Database](https://mlsanity.com/paper/1709.03270/) (2017)
- [Quantum circuit representation of Bayesian networks](https://mlsanity.com/paper/2004.14803/) (2020)

## Built on by (most cited first, 2 of 2)

- [Epistemic Artificial Intelligence is Essential for Machine Learning Models to Truly 'Know When They Do Not Know'](https://mlsanity.com/paper/2505.04950/) (2025)
- [Quantum Information Fusion and Correction under the Transferable Belief Model](https://mlsanity.com/paper/2410.08949/) (2024)

## Abstract (arXiv)

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.