Open Access

REVIEW

Quantum Fuzzy Neural Networks: A Review of Foundations, Modeling Routes, and Open Problems

Yuzhen He¹, Zhiguo Qu^1,2,*, Le Sun¹

1 School of Computer Science, School of Software, Nanjing University of Information Science and Technology, Nanjing, China
2 Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology, Nanjing University of Information Science and Technology, Nanjing, China

* Corresponding Author: Zhiguo Qu. Email:

Journal of Quantum Computing 2026, 8, 55-73. https://doi.org/10.32604/jqc.2026.083993

Received 14 April 2026; Accepted 13 May 2026; Issue published 26 June 2026

Abstract

Quantum fuzzy neural networks (QFNNs) integrate fuzzy systems, neural networks, and quantum models, aiming to leverage their complementary strengths in handling uncertainty, parameter learning, and feature representation. However, a unified framework for effectively combining these three components remains lacking, and the existing literature reflects diverse and sometimes inconsistent modeling strategies. This paper provides a comprehensive review of the fundamental theories underlying QFNNs, including the core design principles and mathematical formulations, as well as the major categories of network architectures. Representative training strategies and typical application scenarios are also systematically examined. Furthermore, persistent issues in the current literature are discussed in detail. These include blurred conceptual boundaries between fuzzy and quantum components, the absence of standardized experimental benchmarks, and the fact that most reported results remain limited to simulated environments without physical validation. Overall, QFNNs are still at an early stage of development and should be regarded as a promising direction for hybrid intelligent modeling rather than an established paradigm.

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Keywords

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