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

Year : 2026 | Volume : 02 | Issue : 01 | Page : 16 21
    By

    Mohammed El Khider,

  • Mohammed Almakki,

  • S. Vairachilai,

  • Markala Karthik,

  1. Assistant Professor, Department of General Undergraduate Curriculum Requirements, University of Dubai, Dubai, United Arab Emirates
  2. Assistant Professor, School of Engineering, Architecture and Interior Design, Amity University Dubai, Dubai, United Arab Emirates
  3. Associate Professor, School of Computer Science and Artificial Intelligence, SR University, Telangana, India
  4. Assistant Professor, Department of Electrical and Electronics Engineering, SR University, Telangana, India

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: Quantum fuzzy logic, tensor operators, multi-qubit systems, state discrimination, symmetry projection, operator algebra

[This article belongs to Emerging Trends in Symmetry ]

How to cite this article:
Mohammed El Khider, Mohammed Almakki, S. Vairachilai, Markala Karthik. Quantum-Fuzzy Tensor Operators for Multi-Qubit Conjunction, Disjunction, and Symmetry-Preserving State Discrimination. Emerging Trends in Symmetry. 2026; 02(01):16-21.
How to cite this URL:
Mohammed El Khider, Mohammed Almakki, S. Vairachilai, Markala Karthik. Quantum-Fuzzy Tensor Operators for Multi-Qubit Conjunction, Disjunction, and Symmetry-Preserving State Discrimination. Emerging Trends in Symmetry. 2026; 02(01):16-21. Available from: https://journals.stmjournals.com/etsy/article=2026/view=247465


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Regular Issue Subscription Original Research
Volume 02
Issue 01
Received 14/03/2026
Accepted 22/04/2026
Published 30/04/2026
Publication Time 47 Days
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