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

Fuzzy Propositional Logic Associated with Quantum Computational Gates

Domenech, G, Freytes, H

Published Dec 26, 2006• 16 citations
OpenAlex

Abstract

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 Poincare structure.

Related papers

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

An Axiomatic System Suggested by Quantum Computation

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.

Journal of Logic and Computation•Feb 27, 2009•0 citations

Quantum computational logic with mixed states

Héctor Freytes, Graciela Domenech

Abstract In this paper we solve the problem how to axiomatize a system of quantum computational gates known as the Poincaré irreversible quantum computational system. A Hilbert‐style calculus is introduced obtaining a strong completeness theorem.

Mathematical logic quarterly•Jan 25, 2013•15 citations

Irreversibility in Quantum Computational Logics

Giuseppe Sergioli, Roberto Giuntini, Francesco Paoli

In this paper we discuss an approach to quantum computation where the basic information units (qubits and quregisters) are replaced by density operators and the restriction to unitary operators as logical gates is lifted through the introduction of the more general concept of quantum operation ( [17], [1]). This perspective is especially suited to provide a physical description of open systems. In particular, we illustrate the advantages of this approach over the standard one and show that it can account for two importantirreversibletransformationsalreadyconsideredintheliterature: theirreversible conjunction IAND and the fuzzy-like Łukasiewicz disjunction⊕.

Applied Mathematics & Information Sciences•Jan 1, 2011•6 citations

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

Fuzzy Propositional Logic Associated with Quantum Computational Gates

Graciela Domenech, Hector Freytes

arXiv:quant-ph/0612211•International Journal of Theoretical Physics•Jan 1, 2006•14 citations
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.
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.
In this paper we discuss an approach to quantum computation where the basic information units (qubits and quregisters) are replaced by density operators and the restriction to unitary operators as logical gates is lifted through the introduction of the more general concept of quantum operation ( [17], [1]). This perspective is especially suited to provide a physical description of open systems. In particular, we illustrate the advantages of this approach over the standard one and show that it can account for two importantirreversibletransformationsalreadyconsideredintheliterature: theirreversible conjunction IAND and the fuzzy-like Łukasiewicz disjunction⊕.
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.