Title: An Adaptive Quantum Circuit of Dempster's Rule of Combination for Uncertain Pattern Classification
Venue: NeurIPS 2025
Accepted: yes
Keywords: Uncertain pattern classification; Quantum evidence theory; Adaptive quantum circuit; Dempster's rule of combination; Quantum amplitude encoding mechanism; Quantum measurement outcome representation
Abstract: In pattern classification, efficient uncertainty reasoning plays a critical role, particularly in real-time applications involving noisy data, ambiguous class boundaries, or overlapping categories. Leveraging the advanced computational power of quantum computing, an Adaptive Quantum Circuit for Dempster’s Rule of Combination (AQC-DRC) is proposed to address efficient classification under uncertain environments. The AQC-DRC is developed within the framework of quantum evidence theory (QET) and facilitates decision-making based on quantum basic probability and plausibility levels, which is a generalized Bayesian inference method. The AQC-DRC provides a deterministic computation of DRC, ensuring that quantum fusion outcomes in uncertain pattern classification are exactly aligned with those of the classical method, while simultaneously achieving exponential reductions in the computational complexity of evidence combination and significantly improving fusion efficiency. It is founded that the quantum basic probability amplitude function in QET, as a generalized quantum probability amplitude, can be naturally utilized to express the quantum amplitude encoding. In addition, the quantum basic probability in QET, as a generalized quantum probability, naturally forms a quantum basic probability distribution and can be used to represent quantum measurement outcomes for quantum basic probability level decision-making. Furthermore, the quantum plausibility function in QET also can be naturally used to express the quantum measurement outcomes for quantum plausibility level decision-making. These findings enrich the physical understanding of quantum amplitude encoding and quantum measurement outcomes, offering broad application prospects for representing and processing uncertain knowledge in pattern classification.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes an Adaptive Quantum Circuit for Dempster's Rule of Combination (AQC-DRC) to address uncertainty in pattern classification. The method leverages quantum evidence theory (QET) to provide efficient evidence fusion while maintaining consistency with classical Dempster-Shafer theory results. The AQC-DRC achieves exponential reductions in computational complexity and supports decision-making based on both quantum basic probability and plausibility levels. The authors present rigorous theoretical derivations, experimental evaluations on datasets such as Iris and Abalone, and a detailed comparison with classical and quantum methods.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\nIn this paper, the authors proposed an Adaptive Quantum Circuit for Dempster’s Rule of Combination (AQC-DRC) to address efficient classification under uncertain environments by leveraging the advanced computational power of quantum computing. The AQC-DRC is developed within the framework of quantum evidence theory (QET) and facilitates decision-making based on quantum basic probability and plausibility levels, which is a generalized Bayesian inference method. The main strengths of this paper are summarized as follows:\n1. The AQC-DRC provides a deterministic computation of DRC, ensuring that quantum fusion outcomes in uncertain pattern classification are exactly aligned with those of the classical method, while simultaneously achieving exponential reductions in the computational complexity of evidence combination and significantly improving fusion efficiency.\n2. It is founded that the quantum basic probability amplitude function in QET, as a generalized quantum probability amplitude, can be naturally utilized to express the quantum amplitude encoding. In addition, the quantum basic probability in QET, as a generalized quantum probability, naturally forms a quantum basic probability distribution and can be used to represent quantum measurement outcomes for quantum basic probability level decision-making. Furthermore, the quantum plausibility function in QET also can be naturally used to express the quantum measurement outcomes for quantum plausibility level decision-making.\n3. These findings enrich the physical understanding of quantum amplitude encoding and quantum measurement outcomes.\nOverall, this work is a generalized Bayesian inference method and is very meaningful to offer broad application prospects for representing and processing uncertain knowledge in pattern classification.\n\nWeaknesses\n1. As the authors mentioned in the paper. The current version of AQC-DRC is unable to process complex-valued input data, thereby constraining its applicability.\n2. Why the quantum plausibility function in QET can be used to represent quantum measurement outcomes for quantum basic probability level decision-making, and can be naturally used to express the quantum measurement outcomes for quantum plausibility level decision-making?\n3. The section of Preliminaries is too long. The content should be concise.\n\nQUESTIONS:\n1. Why the quantum basic probability amplitude function in QET can be naturally utilized to express the quantum amplitude encoding?\n2. What’s different between the quantum basic probability level decision-making and quantum plausibility level decision-making?\n3. Figure A1 is a main flowchart of the adaptive quantum circuit for Dempster’s rule of combination. It should be placed in the main text.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 5, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-06-21"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe manuscript proposes a so-called quantum version of the DS evidence framework, and suggests implementing the model's computation using adaptive quantum circuits. However, there some fundamental misuses in the basic formalization of the manuscript.\n\nSTRENGTHS AND WEAKNESSES:\nIn the main mathematical formalization of the manuscript, there exist misuses (or at least a misleading uses). For example, under the specification of Dirac's bra-ket notation, |ϕ1ϕ2> refers to the simultaneous occurrence of events ϕ1 and ϕ2 on the (two) subsystems of the composite system, respectively. However, the |ϕ1ϕ2> defined in the manuscript (in accordance with the convention of Dempster-Shafer theory) refers to the occurrence of either ϕ1 or ϕ2 on the same system. Overall, although the formalization in the manuscript employs the fundamental formalization of quantum mechanics (Dirac's bra-ket notation), it is contrary to the intrinsic interpretation of the formalization of quantum mechanics in terms of substantive meaning.\n\nBecause this misuse was fundamental, the subsequent formalizations (Definitions 8, 9 and 10, etc.) in the manuscript also deviated from the essential meaning of quantum mechanics. Therefore, the entire formalization of the manuscript and its algorithm model should not be regarded as being quantum in nature. It is merely a heuristic method that shares some formal characteristics with quantum mechanics, but its substantive meaning contradicts the fundamental interpretation of quantum mechanics.\n\nQUESTIONS:\nEssentially, the probabilistic structure corresponding to quantum mechanics is a non-classical probabilistic structure that relaxes the closure property of sigma algebra with respect to countable unions in Kolmogorov's probability axioms. Does the authors of the paper know that this structure is not isomorphic to the mathematical structure underlying the DS theory, and therefore cannot be directly expressed in a quantum formalism?\n\nLIMITATIONS:\nEssentially, the probabilistic structure corresponding to quantum mechanics is a non-classical probabilistic structure that relaxes the closure property of sigma algebra with respect to countable unions in Kolmogorov's probability axioms. Does the authors of the paper know that this structure is not isomorphic to the mathematical structure underlying the DS theory, and therefore cannot be directly expressed in a quantum formalism?", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-24"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors propose an Adaptive Quantum Circuit for Dempsters Rule of Combination (AQC-DRC) calculations in Dempster-Shafer (DS) theory of evidence which combines two basic probability assignments (BPA).  After defining basic DS concepts such as evidence, plausibility, BBA, etc. in quantum terms, the lay out their Adaptive Quantum Circuit which consists of a quantum amplitude encoding for BPA, a construction of the adaptive quantum circuit for DRC, and a measurement in the adaptive quantum circuit for subsequent decision-making.  They implement methods for basic probability and plausibility with the AQC-DRC.  They evaluate their quantum system on three classification datasets comparing their approach with the classical DS classification and show that the quantum methods gradually approach the classical results as the number of measurement shots increases while achieving an exponential speedup over classical methods.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\nThe mapping of classical DRC into a quantum framework and then showing the viability and exponential speedup without significant loss of accuracy is important for the future when quantum computers will have evolved to a point where the are available for performing the types of classifications tasks the authors discuss.\n\nWeakness:\n\nThe DRC is know to be problematic and I wonder if the authors could also implement the Fagin-Halpern conditional which provides a better method for information fusion without the problems of the DCR.  It would have been also good to discuss any potential near-term applications of their AQC-DRC.\n\nQUESTIONS:\nHave you thought about mapping conditional beliefs and plausibilities into the quantum framework, i.e., Bl(A|B) and Pl(A|B)?  These are particularly useful as lower and upper bounds for Bayesian conditionals P(A|B).  Also, can you please clarify how you arrived at the various quantum complexity results?\n\nLIMITATIONS:\nI would move the limitations section to the regular text", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 1, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nTo address efficient classification under uncertain environments, the authors proposed an adaptive quantum circuit for Dempster’s rule of combination (AQC-DRC) to support quantum basic probability and plausibility level decision-making within the framework of quantum evidence theory (QET).\n\nSTRENGTHS AND WEAKNESSES:\nStrengths：-- The AQC-DRC, as a generalized quantum Bayesian inference method, enabled deterministic computation of DRC, ensuring that quantum fusion outcomes in uncertain pattern classification are fully consistent with those of the classical method.\n-- Furthermore, the proposed AQC-DRC achieved an exponential reduction in computational complexity, positioning it as a promising approach for real-time quantum multisource information fusion.\n-- The architecture of the proposed AQC-DRC is conceptually straightforward and highly scalable, which facilitates its practical implementation.\n-- The quantum basic probability amplitude function in QET can naturally express the quantum amplitude encoding. The quantum basic probability in QET, forming the quantum basic probability distribution, can directly express quantum measurement outcomes for basic probability level decision-making, while the quantum plausibility function in QET can also naturally represent the quantum measurement outcomes for plausibility-level decision-making.\n-- These insights not only broaden the understanding of QET, but also provide a more intuitive physical interpretation of quantum amplitude encoding and quantum measurement outcomes.\nWeaknesses：\nDue to the limitations of quantum hardware, the proposed AQC-DRC is unable to handle high-dimensional data.\n\nQUESTIONS:\n1. What are the QC-DRC_QBP + QPl and AQC-DRC_QBP + QPl? The methods of QC-DRC_QBP + QPl and AQC-DRC_QBP + QPl should be explained in the text.\n2. What are the purpose of two decision-making levels of quantum basic probability and quantum plausibility?\n3. In what situations are quantum basic probability and quantum plausibility used?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 5, "CLARITY": 4, "IMPACT": 4, "ORIGINALITY": 4, "DATE": "2025-07-06"}