Book ChapterDOI
Quantum logic and automata theory
Mingsheng Ying
- pp 619-754
TLDR
This chapter describes a systematic exposition of automata theory, and defines the classes of languages accepted—namely, orthomodular lattice-valued regular languages and context-free languages.Abstract:
Publisher Summary It is noted that a theory of computation based on quantum logic is to be established as a logical foundation of quantum computation. Finite automata and pushdown automata are considered the simplest abstract mathematical models of computing machines. Automata theory is an essential part of computation theory. This chapter describes a systematic exposition of automata theory. In context to this theory, quantum logic is treated as an orthomodular lattice-valued logic. The approach employed in developing this theory is essentially the semantical analysis. This chapter introduces notions of orthomodular lattice-valued finite automata and pushdown automata and their various variants. It defines the classes of languages accepted—namely, orthomodular lattice-valued regular languages and context-free languages. This chapter also re-examines various properties of automata in the framework of quantum logic, including the Kleene theorem concerning equivalence between finite automata and regular expressions, equivalence between pushdown automata and context-free grammars, and the pumping lemma both for regular languages and for context-free languages.read more
Citations
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Journal ArticleDOI
Quantum computation, quantum theory and AI
TL;DR: The author hopes that this paper will be a useful map for AI researchers who are going to explore further and deeper connections between AI and quantum computation as well as quantum theory although some parts of the map are very rough and other parts are empty, and waiting for the readers to fill in.
BookDOI
Semantic Techniques in Quantum Computation
TL;DR: This book explores quantum computation from the perspective of the branch of theoretical computer science known as semantics, as an alternative to the more well-known studies of algorithmics, complexity theory, and information theory.
Journal ArticleDOI
Model-Checking Linear-Time Properties of Quantum Systems
TL;DR: An automata-based model-checking technique is generalized for the verification of safety properties recognizable by reversible automata and ω--properties recognizing by reversible Büchi automata.
Book ChapterDOI
Predicate Transformer Semantics of Quantum Programs
TL;DR: In this paper, a predicate transformer semantics for quantum programs is presented, and the universal conjunctivity and termination law of quantum programs are proved, and Hoare's induction rule is established in the quantum setting.
Journal ArticleDOI
Quantum programming: From theories to implementations
TL;DR: This paper surveys the new field of programming methodology and techniques for future quantum computers, including design of sequential and concurrent quantum programming languages, their semantics and implementations.
References
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Journal ArticleDOI
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
TL;DR: In this paper, the authors considered factoring integers and finding discrete logarithms on a quantum computer and gave an efficient randomized algorithm for these two problems, which takes a number of steps polynomial in the input size of the integer to be factored.
Journal ArticleDOI
Simulating physics with computers
TL;DR: In this paper, the authors describe the possibility of simulating physics in the classical approximation, a thing which is usually described by local differential equations, and the possibility that there is to be an exact simulation, that the computer will do exactly the same as nature.
Proceedings ArticleDOI
A fast quantum mechanical algorithm for database search
TL;DR: In this paper, it was shown that a quantum mechanical computer can solve integer factorization problem in a finite power of O(log n) time, where n is the number of elements in a given integer.
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.