STUDIES IN QUDITS-BASED MULTI-VALUED QUANTUM COMPUTATIONAL LOGIC

The thesis aims to analyze the circuit model of quantum computation, from a fuzzy logico-algebraic perspective, by employing a technique of continuous t-norm based fuzzy polynomial residuation of some of the important building-blocks of quantum circuits involving qudits. The thesis builds upon the previous works on the framework of Quantum Computational Logic, representing the quantum computational operations in general in terms of the ‘Lukasiewicz sum’ (x ⊕ y = min{x + y, 1}), ‘Lukasiewicz negation’ (¬x = 1 − x), and a ‘product t-norm’ (x · y), forming what is known as a ‘product Mv-algebra’. The framework is extended here to the qudit based quantum computational schemes, as the qudits based schemes are yet more nontrivial than even the qubits based schemes – due to the well known non-trivialities of the (d>2) higher-dimensional Hilbert Spaces. Employing a novel unitary gate construction recipe in a qudits-based multi-valued logical setting, the work constructs and investigates generalized quantum versions of the logical-gate-operations of Negation (and its square-root), Hadamard, Swap, as well as those due to Toffoli and Fredkin. It is hoped that the work will be of utility in constructing and interpreting the quantum computational schemes further, –especially from (but not limited to) logico-algebraic perspectives.