Open AccessPosted Content
Paraconsistent Machines and their Relation to Quantum Computing
Juan C. Agudelo,Walter Carnielli +1 more
Reads0
Chats0
TLDR
Paraconsistent Turing machines as discussed by the authors allow a partial simulation of superposed states of quantum computing, allowing the definition of paraconsistent algorithms which solve Deutsch's and Deutsch-Jozsa problems.Abstract:
We describe a method to axiomatize computations in deterministic Turing machines. When applied to computations in non-deterministic Turing machines, this method may produce contradictory (and therefore trivial) theories, considering classical logic as the underlying logic. By substituting in such theories the underlying logic by a paraconsistent logic we define a new computation model, the paraconsistent Turing machine. This model allows a partial simulation of superposed states of quantum computing. Such a feature allows the definition of paraconsistent algorithms which solve (with some restrictions) the well-known Deutsch's and Deutsch-Jozsa problems. This first model of computation, however, does not adequately represent the notions of entangled states and relative phase, which are key features in quantum computing. In this way, a more sharpened model of paraconsistent Turing machines is defined, which better approaches quantum computing features. Finally, we define complexity classes for such models, and establish some relationships with classical complexity classes.read more
Citations
More filters
Proceedings ArticleDOI
Quantum processes: A new interpretation for quantum transformations in the VPE-qGM environment
TL;DR: The main contribution of this work consists in designing optimizations resulting from the description of quantum transformations using Quantum Processes and Partial quantum Processes conceived in the qGM theoretical model, allowing the simulation of more complex quantum algorithms.
Proceedings ArticleDOI
Paraconsistent Transition Systems
TL;DR: Paraconsistent transition systems are proposed in this article as one such formalism: states evolve through two accessibility relations capturing weighted evidence of a transition or its absence, respectively, their weights come from a specific residuated lattice.
References
More filters
Book
Quantum Computation and Quantum Information
TL;DR: In this article, the quantum Fourier transform and its application in quantum information theory is discussed, and distance measures for quantum information are defined. And quantum error-correction and entropy and information are discussed.
Book
Introduction to Automata Theory, Languages, and Computation
TL;DR: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity, appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.
Journal ArticleDOI
On Computable Numbers, with an Application to the Entscheidungsproblem
TL;DR: This chapter discusses the application of the diagonal process of the universal computing machine, which automates the calculation of circle and circle-free numbers.
Journal ArticleDOI
Quantum theory, the Church-Turing principle and the universal quantum computer
TL;DR: In this paper, it is argued that underlying the Church-Turing hypothesis there is an implicit physical assertion: every finitely realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means.
Journal ArticleDOI
Logical reversibility of computation
TL;DR: This result makes plausible the existence of thermodynamically reversible computers which could perform useful computations at useful speed while dissipating considerably less than kT of energy per logical step.
Related Papers (5)
Paraconsistent Machines and their Relation to Quantum Computing
Juan C. Agudelo,Walter Carnielli +1 more