Fuzzy approach to quantum Fredkin gate

In the framework of quantum computation with mixed states, we introduce a fuzzy approach to the quantum Fredkin gate. Under this perspective, we investigate the behaviour of the gate applied to factorized and non-factorized quantum states.

[1]  Roberto Giuntini,et al.  Holistic logical arguments in quantum computation , 2016, 1602.07516.

[2]  R. Giuntini,et al.  Entanglement and Quantum Logical Gates. Part I. , 2015 .

[3]  Franco Montagna,et al.  Product logic and probabilistic Ulam games , 2007, Fuzzy Sets Syst..

[4]  Hector Freytes,et al.  Representing continuous t-norms in quantum computation with mixed states , 2010 .

[5]  Marcelo Simoes.  Introduction to Fuzzy Control , 2003 .

[6]  Stan Gudder,et al.  Quantum Computational Logic , 2003 .

[7]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[8]  Roberto Giuntini,et al.  Reasoning in Quantum Theory: Sharp and Unsharp Quantum Logics , 2010 .

[9]  Daniele Mundici.  Ulam Games, Lukasiewicz Logic, and AF C*-Algebras , 1993, Fundam. Informaticae.

[10]  Francesco Paoli,et al.  Some generalizations of fuzzy structures in quantum computational logic , 2011, Int. J. Gen. Syst..

[11]  Roberto Giuntini,et al.  Reasoning in quantum theory , 2004 .

[12]  Hector Freytes,et al.  Fuzzy Type Representation of the Fredkin Gate in Quantum Computation with Mixed States , 2017 .

[13]  Hector Freytes,et al.  Fuzzy Propositional Logic Associated with Quantum Computational Gates , 2006 .

[14]  Hector Freytes,et al.  Quantum computational logic with mixed states , 2010, Math. Log. Q..

[15]  Noam Nisan,et al.  Quantum circuits with mixed states , 1998, STOC '98.

[16]  T. Toffoli,et al.  Conservative logic , 2002, Collision-Based Computing.

[17]  Schlienz,et al.  Description of entanglement. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[18]  Petr Hájek,et al.  Metamathematics of Fuzzy Logic , 1998, Trends in Logic.

[19]  F. Montagna.  Functorial Representation Theorems for MVΔ Algebras with Additional Operators , 2001 .

[20]  Ján Jakubík,et al.  On Product MV-Algebras , 2002 .