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IEEE International Conference on Computational Cybernetics (ICCC)

Emulating Quantum Interference and Quantum Associative Memory Using Fuzzy Qubits

M. Skander Hannachi, Fangyan Dong, Kaoru Hirota

Published Oct 1, 2007• 5 citations
Publisher

Abstract

The concept of fuzzy qubit is proposed as an approach to emulating quantum interference using fuzzy logic. This makes it possible to implement certain quantum computing algorithms, especially quantum associative memory, on hardware dedicated to fuzzy logic. The fuzzy qubit model is briefly reviewed and the fuzzy implementation of basic 1 and 2 qubit gates, such as Hadamard or C-not gates, is presented. The possibility of emulating quantum algorithms is discussed. Then quantum associative memory is presented and its implementation using the fuzzy qubit model is discussed. The advantages over the previous associative memory models, both quantum and classical, are discussed.

DOI
10.1109/icccyb.2007.4402017

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The concept of fuzzy qubit is proposed as an approach to emulating quantum interference using fuzzy logic. This makes it possible to implement certain quantum computing algorithms, especially quantum associative memory, on hardware dedicated to fuzzy logic. The fuzzy qubit model is briefly reviewed and the fuzzy implementation of basic 1 and 2 qubit gates, such as Hadamard or C-not gates, is presented. The possibility of emulating quantum algorithms is discussed. Then quantum associative memory is presented and its implementation using the fuzzy qubit model is discussed. The advantages over the previous associative memory models, both quantum and classical, are discussed.
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Abstract In the paper we suggest a system of fuzzy Tsetlin automata for analog computations. The system deals with fuzzy analogs of qubits and models operations of quantum gates used for quantum computations. In contrast to the existing models, the suggested system directly emulates reversible operators and the “square root of not” operator which is a key operator in quantum computations. Fuzzy information units called f-bits are defined by matrix with fuzzy normalized rows and emulate qubits with complex elements. Operations with these units are conducted by fuzzy Tsetlin automata based on the uninorm and absorbing norm. It is demonstrated that the suggested system emulates basic quantum computations; hence, it can implement analog computations and can support analog emulations of quantum algorithms.
The emerging research area of a quantum-inspired computing has been applied to various field such as computational intelligence, and showed its superior abilities. However, most existing researches are focused on theoretical simulations, and have not been implemented in systems under practical environment. For human–robot communication, associative memory becomes essential for multi-modal communication. However, it always suffers from low memory capacity and recall reliability. In this paper, we propose a quantum-inspired bidirectional associative memory with fuzzy inference. We show that fuzzy inference satisfies basic postulates of quantum mechanics, but also learning algorithm for weight matrix in associative memory. In addition, we construct a communication system with robot partner using proposed model. This is the first successful attempt to overcome conventional problems in associative memory model with a robot application.
This paper shows that quantum computing extends the class of fuzzy sets, taking advantage of properties such as quantum parallelism. The central idea associates the states of a quantum register with membership functions of fuzzy subsets, and the rules for the processes of fuzzyfication are performed by unitary quantum transformations. Besides studying the construction of logical operators, such as negation, using quantum, this paper also introduces the definition of t-norms and t-conorms based on unitary and controlled quantum gates. Such constructors allow modelling and interpreting union, intersection and difference between fuzzy sets. As the main contribution, an interpretation for the Reichenbach implication from quantum computing is obtained. An evaluation of the corresponding computation is implemented and simulated in the VPE-qGM visual programming environment.
In this paper we present our proposal for a fuzzy logic model based on Quantum Computing. After analyzing how logical connectives are constructed and applied in fuzzy logic, we research how Quantum Computing can provide a new model to manage fuzzy variables, mainly using superposition of states for the implementation of fuzzy information. A comparison between our proposal and several classical connectives is carried out, including negation, conjunction and disjunction. We prove that quantum fuzzy connectives present a proper behavior, manifesting the peculiarities of the quantum paradigm, which is beneficial for the representation of uncertain knowledge. We conclude on how this work establishes a model that can be further expanded for the development of quantum fuzzy reasoning.