Fuzzy representation of finite-valued quantum gates

The theory of logical gates in quantum computation has inspired the development of new forms of quantum logic based on the following semantic idea: the meaning of a formula is identified with a quantum information quantity, represented by a density operator. At the same time, the logical connectives...

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Bibliographic Details
Published in:Soft computing (Berlin, Germany) Germany), 2020-07, Vol.24 (14), p.10305-10313
Main Authors: Leporini, Roberto, Bertini, Cesarino, Fabiani, Filippo Carone
Format: Article
Language:English
Subjects:
Algebra
Artificial Intelligence
Computational Intelligence
Control
Eigenvalues
Eigenvectors
Energy
Engineering
Focus
Fuzzy logic
Gates
Hilbert space
Logic circuits
Mathematical Logic and Foundations
Mechatronics
Operators (mathematics)
Quantum computing
Quantum phenomena
Representations
Robotics
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Summary:The theory of logical gates in quantum computation has inspired the development of new forms of quantum logic based on the following semantic idea: the meaning of a formula is identified with a quantum information quantity, represented by a density operator. At the same time, the logical connectives are interpreted as operations defined in terms of quantum gates. In this framework, some possible relations between fuzzy representations based on continuous t -norms for quantum gates and the probabilistic behavior of quantum computational finite-valued connectives are investigated. In particular, a fuzzy-type representation for quantum many-valued extensions of the gates introduced by Toffoli, Fredkin and Peres is described.
ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-020-04870-3