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Logical and algebraic structures from Quantum Computation

Ledda, Antonio (2008) Logical and algebraic structures from Quantum Computation. [Doctoral Thesis]



The main motivation for this thesis is given by the open problems regarding the axiomatisation of quantum computational logics. This thesis will be structured as follows: in Chapter 2 we will review some basics of universal algebra and functional analysis. In Chapters 3 through 6 the fundamentals of quantum gate theory will be produced. In Chapter 7 we will introduce quasi-MV algebras, a formal study of a suitable selection of algebraic operations associated with quantum gates. In Chapter 8 quasi-MV algebras will be expanded by a unary operation hereby dubbed square root of the inverse, formalising a quantum gate which allows to induce entanglement states. In Chapter 9 we will investigate some categorial dualities for the classes of algebras introduced in Chapters 7 and 8. In Chapter 10 the discriminator variety of linear Heyting quantum computational structures, an algebraic counterpart of the strong quantum computational logic, will be considered. In Chapter 11, we will list some open problems and, at the same time, draw some tentative conclusions. Lastly, in Chapter 12 we will provide a few examples of the previously investigated structures.

Item Type:Doctoral Thesis
Date:06 February 2008
Tutor:Giuntini, Roberto, Paoli, Francesco
PhD classes:Ciclo 20 > Storia, filosofia e didattica delle scienze
Institution:Universita' degli Studi di Cagliari
Divisions:Dipartimenti (fino a dicembre 2011) > Dipartimento di Scienze pedagogiche e filosofiche
Subjects:Area 11 - Scienze storiche, filosofiche, pedagogiche e psicologiche > M-FIL/02 Logica e filosofia della scienza
Uncontrolled Keywords:Quantum Computation, Quasi-MV Algebras
ID Code:41
Deposited On:28 Oct 2008 09:09

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