A note on many valued quantum computational logics

Abstract

The standard theory of quantum computation relies on the idea that the basic information quantity is represented by a superposition of elements of the canonical basis and the notion of probability naturally follows from the Born rule. In this work we consider three valued quantum computational logics. More specifically, we will focus on the Hilbert space C 3 , we discuss extensions of several gates to this space and, using the notion of effect probability, we provide a characterization of its states.

Binary Gates in Three Valued Quantum Computational Logics

“…-enquiring into the logical properties of 3-valued quantum computational logics through the notion of effect probability [13];…”

“…In [2,13] authors proposed an extension of the standard quantum computational logic where the basic information quantity is a qutrit (a unit vector of the Hilbert space C 3 ) instead of the usual qubit. Following this approach, the standard quantum computational basis is replaced by the three-valued quantum computational basis B (3) = {|0 , | 1 2 , |1 }, and in this context several unary quantum gates were discussed.…”

Quantum circuit optimization for unitary operators over non-adjacent qudits

“…The quantum computational theory has naturally inspired new forms of quantum logic, the so called quantum computational logic [6,7,14,24]. From a semantic point of view, any formula of the language in the QCL denotes a piece of quantum information, i.e.…”