Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Computer Science & Systems Biology

Fuzzy Implementation of Qubits Operators

Alexander Rybalov, Eugene Kagan

Published Jan 1, 2014• 9 citations
Publisher

Abstract

In the paper, a complete minimal system of fuzzy logic operators that implements the operations over qubits is suggested.The model is based on a parametric system of the fuzzy not and phase operators and represents operators of quantum information theory acting on real amplitudes.An example of the system application is provided by its implementation to a mobile robot control, and its correspondence with the previously suggested models is illustrated by numerical simulations.

DOI
10.4172/jcsb.1000151

Related papers

Fuzzy Tsetlin automata and their application in analog computing

Eugene Kagan, Alexander Rybalov

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.

Soft Computing•Apr 29, 2026•0 citations

Fuzzy model of control for quantum-controlled mobile robots

Alexander Rybalov, Eugene Kagan, Yochai Manor +1 more

In this work we consider a navigation of quantum-controlled mobile robot by the use of fuzzy methods. A fuzzy model of the robot behavior is obtained by transformation of the robot's states (that appear in a form of qubits) into the pairs of membership functions. For a full description of the robot's turns, we define a reverse fuzzy Hadamard operator that completes the known Hannachi, Hatakeyama and Hirota model. The suggested transformations and methods were comparatively studied by field trials using small mobile robots and by numerical simulations that model the robot's behavior in the presence of noise.

IEEE Convention of Electrical and Electronics Engineers in Israel•Nov 1, 2010•10 citations

Quantum Computational Fuzzy Logics

Cesarino Bertini, Roberto Leporini

The theory of logical gates in quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister (a system of qubits in a pure state) or, more generally, with a mixture of quregisters (called qumix). Following an approach proposed by Domenech and Freytes, we apply residuated structures associated with fuzzy logic to develop certain aspects of information processing in quantum computing from a logical perspective. For this purpose, we introduce an axiomatic system whose natural interpretation is the irreversible quantum Poincaré algebra. Such a system allows to establish a completeness theorem for the treatment of quantum information.

•Jan 1, 2007•0 citations

The Fuzzy Bit

Milagrosa Aldana, M. A. Lledó

In this paper, the formulation of Quantum Mechanics in terms of fuzzy logic and fuzzy sets is explored. A result by Pykacz, which establishes a correspondence between (quantum) logics (lattices with certain properties) and certain families of fuzzy sets, is applied to the Birkhoff–von Neumann logic, the lattice of projectors of a Hilbert space. Three cases are considered: the qubit, two qubits entangled, and a qutrit ‘nested’ inside the two entangled qubits. The membership functions of the fuzzy sets are explicitly computed and all the connectives of the fuzzy sets are interpreted as operations with these particular membership functions. In this way, a complete picture of the standard quantum logic in terms of fuzzy sets is obtained for the systems considered.

arXiv:2311.14083•Symmetry•Nov 23, 2023•1 citation

Fuzzy-processing quantum computation

Yan-Xiong Du

Quantum computation has attracted numerous attentions and develops rapidly in the recent decades. To against the decoherence and the control errors upon the qubits, quantum error corrections are adopted. Such approaches require lots of redundant qubits, accurate measurement and timely feedback. Here we investigate a new framework of quantum computation that is associated with fuzzy processing. It will benefit significantly from three aspects: the fuzzy recognition of qubit states reduce the required gate fidelity; the fuzzy encoding encodes the information of the qubits into a distribution of probability, suppressing the fluctuations in the output of long quantum circuits; the fuzzy feedback offers a more efficient way to control the qubits when precision information of quantum states are absent. Furthermore, the fuzzy processing can be integrated into quantum error correction, eliminating the need for immediate correction operations. The proposed scheme will be fairly suitable for the solution of decision problems, which has significant applications in the optimization problems and control problems.

quant-pharXiv:2606.16623•Jun 16, 2026•0 citations

Emulating Quantum Interference and Quantum Associative Memory Using Fuzzy Qubits

M. Skander Hannachi, Fangyan Dong, Kaoru Hirota

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.

IEEE International Conference on Computational Cybernetics (ICCC)•Oct 1, 2007•5 citations
In the paper, a complete minimal system of fuzzy logic operators that implements the operations over qubits is suggested.The model is based on a parametric system of the fuzzy not and phase operators and represents operators of quantum information theory acting on real amplitudes.An example of the system application is provided by its implementation to a mobile robot control, and its correspondence with the previously suggested models is illustrated by numerical simulations.
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.
In this work we consider a navigation of quantum-controlled mobile robot by the use of fuzzy methods. A fuzzy model of the robot behavior is obtained by transformation of the robot's states (that appear in a form of qubits) into the pairs of membership functions. For a full description of the robot's turns, we define a reverse fuzzy Hadamard operator that completes the known Hannachi, Hatakeyama and Hirota model. The suggested transformations and methods were comparatively studied by field trials using small mobile robots and by numerical simulations that model the robot's behavior in the presence of noise.
The theory of logical gates in quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister (a system of qubits in a pure state) or, more generally, with a mixture of quregisters (called qumix). Following an approach proposed by Domenech and Freytes, we apply residuated structures associated with fuzzy logic to develop certain aspects of information processing in quantum computing from a logical perspective. For this purpose, we introduce an axiomatic system whose natural interpretation is the irreversible quantum Poincaré algebra. Such a system allows to establish a completeness theorem for the treatment of quantum information.
In this paper, the formulation of Quantum Mechanics in terms of fuzzy logic and fuzzy sets is explored. A result by Pykacz, which establishes a correspondence between (quantum) logics (lattices with certain properties) and certain families of fuzzy sets, is applied to the Birkhoff–von Neumann logic, the lattice of projectors of a Hilbert space. Three cases are considered: the qubit, two qubits entangled, and a qutrit ‘nested’ inside the two entangled qubits. The membership functions of the fuzzy sets are explicitly computed and all the connectives of the fuzzy sets are interpreted as operations with these particular membership functions. In this way, a complete picture of the standard quantum logic in terms of fuzzy sets is obtained for the systems considered.
Quantum computation has attracted numerous attentions and develops rapidly in the recent decades. To against the decoherence and the control errors upon the qubits, quantum error corrections are adopted. Such approaches require lots of redundant qubits, accurate measurement and timely feedback. Here we investigate a new framework of quantum computation that is associated with fuzzy processing. It will benefit significantly from three aspects: the fuzzy recognition of qubit states reduce the required gate fidelity; the fuzzy encoding encodes the information of the qubits into a distribution of probability, suppressing the fluctuations in the output of long quantum circuits; the fuzzy feedback offers a more efficient way to control the qubits when precision information of quantum states are absent. Furthermore, the fuzzy processing can be integrated into quantum error correction, eliminating the need for immediate correction operations. The proposed scheme will be fairly suitable for the solution of decision problems, which has significant applications in the optimization problems and control problems.
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.