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Emerging Trends in Symmetry Original Research

Quantum-Fuzzy Tensor Operators for Multi-Qubit Conjunction, Disjunction, and Symmetry-Preserving State Discrimination

  1. Mohammed El Khider Department of General Undergraduate Curriculum Requirements, University of Dubai
  2. Mohammed Almakki School of Engineering, Architecture and Interior Design, Amity University Dubai
  3. S. Vairachilai School of Computer Science and Artificial Intelligence, SR University
  4. Markala Karthik Department of Electrical and Electronics Engineering, SR University

Abstract

The integration of fuzzy logic and quantum information theory raises a fundamental mathematical question: how can degrees of truth be encoded in multi-qubit amplitudes while preserving the unitary dynamics and symmetry structure of quantum state spaces? This paper develops a tensor-operator framework for implementing quantum-fuzzy logical operations on finite qubit registers. Fuzzy truth values are represented by normalized quantum amplitude pairs, enabling logical information to be embedded directly into quantum states. Logical conjunction and disjunction are realized through block-unitary tensor operators acting on computational basis states augmented by ancilla qubits. Explicit closed-form constructions are derived for conjunction, disjunction, and controlled complement operators. These operators preserve normalization and admit implementation within standard quantum-circuit architectures. We prove that, after measurement and appropriate renormalization, the expectation values induced by the proposed operators reproduce the behavior of fuzzy t-norms and t-conorms, establishing a rigorous correspondence between quantum-state evolution and fuzzy logical aggregation. To ensure compatibility with exchange symmetries that arise naturally in multi-qubit systems, a permutation-symmetry projector is introduced. This projector restricts the dynamics to exchange-invariant subspaces while maintaining the logical interpretation of the encoded fuzzy values. We further demonstrate that the projected logical operators possess reduced-dimensional representations on symmetric tensor powers, leading to more efficient realizations and analysis. The resulting framework provides a mathematically consistent bridge between fuzzy reasoning and quantum computation, unifying probabilistic truth representation, tensor-algebraic operator design, and symmetry-preserving quantum dynamics. These results offer a foundation for the development of quantum-fuzzy information processing, logical inference, and decision-making models in quantum computational environments.

Keywords

References (25)

  1. Bertini C, Leporini R. A fuzzy approach to quantum logical computation. Fuzzy Sets and Systems. 2017;317:44-60. doi:10.1016/j.fss.2016.06.004
  2. Ishikawa S, Kikuchi K. Quantum Fuzzy Logic and Time. Journal of Applied Mathematics and Physics. 2021;09(11):2609-2622. doi:10.4236/jamp.2021.911168
  3. Singh AK, Singh R, Singh B. Quantum Logics of Fuzzy Representations. New Mathematics and Natural Computation. 2024;21(03):1047-1064. doi:10.1142/s1793005725500504
  4. Dai S. On the quantum circuit implementation of fuzzy reasoning. Fuzzy Sets and Systems. 2026;522:109611. doi:10.1016/j.fss.2025.109611
  5. Acampora G, Schiattarella R, Vitiello A. On the Implementation of Fuzzy Inference Engines on Quantum Computers. IEEE Transactions on Fuzzy Systems. 2023;31(5):1419-1433. doi:10.1109/tfuzz.2022.3202348
  6. Acampora G, Grossi M, Schenk M, Schiattarella R. Quantum Fuzzy Inference Engine for Particle Accelerator Control. IEEE Transactions on Quantum Engineering. 2024;5:1-13. doi:10.1109/tqe.2024.3374251
  7. Acampora G, Schiattarella R, Vitiello A. Using quantum fuzzy inference engines in smart cities. In: 2024 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). 2024:1–8. doi:10.1109/FUZZ- IEEE60900.2024.10611863.
  8. Nunziata G, Crisci S, De Gregorio G, Schiattarella R, Acampora G, Coraggio L, et al. Quantum fuzzy logic for edge detection: A demonstration on NISQ hardware. Applied Soft Computing. 2025;185:113866. doi:10.1016/j.asoc.2025.113866
  9. Khushal R, Fatima DU. Fuzzy quantum machine learning (FQML) logic for optimized disease prediction. Computers in Biology and Medicine. 2025;192:110315. doi:10.1016/j.compbiomed.2025.110315
  10. Marín Díaz G. Fuzzy C-Means and Explainable AI for Quantum Entanglement Classification and Noise Analysis. Mathematics. 2025;13(7):1056. doi:10.3390/math13071056
  11. Yogeesh N, Sayed A. Theoretical framework of quantum perspectives on fuzzy mathematics: unveiling neural mechanisms of consciousness and cognition. NeuroQuantology. 2017;15(4):180–187. doi:10.48047/nq.2017.15.4.1148.
  12. Yogeesh N, et al. Quantum implementation of fuzzy logic conjunction and disjunction using multiqubit gates. European Chemical Bulletin. 2023;12(5):2098–2108. doi:10.48047/ecb/2023.12.5.145.
  13. Zadeh LA. Fuzzy sets. Information and Control. 1965;8(3):338-353. doi:10.1016/s0019-9958(65)90241-x
  14. Mamdani EH, Assilian S. An experiment in linguistic synthesis with a fuzzy logic controller. International Journal of Man-Machine Studies. 1975;7(1):1-13. doi:10.1016/s0020-7373(75)80002-2
  15. Jang JSR. ANFIS: adaptive-network-based fuzzy inference system. IEEE Transactions on Systems, Man, and Cybernetics. 1993;23(3):665-685. doi:10.1109/21.256541
  16. Mendel JM. Fuzzy logic systems for engineering: a tutorial. Proceedings of the IEEE. 1995;83(3):345-377. doi:10.1109/5.364485
  17. Acampora G, Vitiello A. Error Mitigation in Quantum Measurement through Fuzzy C-Means Clustering. 2021 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). 2021:1-6. doi:10.1109/fuzz45933.2021.9494538
  18. Yogeesh N, Girija DK, William P, Rashmi M. Improving Speech Privacy with Fuzzy Logic-Based Encryption. 2023 IEEE 2nd International Conference on Industrial Electronics: Developments & Applications (ICIDeA). 2023:217-222. doi:10.1109/icidea59866.2023.10295183
  19. Maximizing Efficiency using Fuzzy Matrix Optimization for Wireless Resource Allocation. Applied Mathematics & Information Sciences. 2024;18(6):1495-1506. doi:10.18576/amis/180625
  20. Optimizing MIMO Antenna Performance Using Fuzzy Logic Algorithms. Applied Mathematics & Information Sciences. 2025;19(2):349-364. doi:10.18576/amis/190211
  21. Leveraging Fuzzy Logic for Habitat Suitability Analysis: A Comprehensive Case Study in Digital Ecosystems. Applied Mathematics & Information Sciences. 2025;19(2):335-347. doi:10.18576/amis/190210
  22. Suleiman Mohammad, Yogeesh N, Khaleel Ibrahim Al-Daoud, N Raja, Manoj C R, Raghavendra M H, Asokan Vasudevan, et al. A Mathematical Fuzzy Model for Syntax-Pragmatics Interface. Forum for Linguistic Studies. 2025;7(6). doi:10.30564/fls.v7i6.9618
  23. Yogeesh N, et al. Fuzzy logic-based beat tracking in music signals. Musik in Bayern. 2023. doi:10.15463/gfbm-mib-2023-343.
  24. Yogeesh N, Divyashree J, Girija DK, Rashmi M. Enhancing crop protection and yield with nanotechnology : A Fuzzy mathematical approach. Biochemical and Cellular Archives. 2023;23(2). doi:10.51470/bca.2023.23.2.881
  25. Nigusie AM. Reducing the Effect of Uncertainty in Mamdani–Type Fuzzy Inference System Using Qubits. Journal of Uncertain Systems. 2024;17(04). doi:10.1142/s175289092450020x
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