Termination of nondeterministic quantum programs

We define a language-independent model of nondeterministic quantum programs in which a quantum program consists of a finite set of quantum processes. These processes are represented by quantum Markov chains over the common state space, which formalize the quantum mechanical behaviors of the machine....

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Bibliographic Details
Published in:Acta informatica Vol. 51; no. 1; pp. 1 - 24
Main Authors: Li, Yangjia, Yu, Nengkun, Ying, Mingsheng
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2014
Springer
Springer Nature B.V
Subjects:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Computer Science
Computer science; control theory; systems
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Exact sciences and technology
Hilbert space
Information Systems and Communication Service
Law
Logics and Meanings of Programs
Markov analysis
Markov chains
Mathematical analysis
Mathematical models
Mathematics
Miscellaneous
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Original Article
Probability
Programming languages
Quantum mechanics
Quantum theory
Sciences and techniques of general use
Semantics
Software Engineering/Programming and Operating Systems
Studies
Theoretical computing
Theory of Computation
World
User
Computer theory
Necessary and sufficient condition
Probability
Termination
State space
Probability distribution
State space method
Checking program
Zero one law
Algorithm
Markov chain
Behavior
ISSN:0001-5903, 1432-0525
Online Access:Get full text
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Summary:We define a language-independent model of nondeterministic quantum programs in which a quantum program consists of a finite set of quantum processes. These processes are represented by quantum Markov chains over the common state space, which formalize the quantum mechanical behaviors of the machine. An execution of a nondeterministic quantum program is modeled by a sequence of actions of individual processes, and at each step of an execution a process is chosen nondeterministically to perform the next action. This execution model formalize the users’ behavior of calling the processes in the classical world. Applying the model to a quantum walk as an instance of physically realizable systems, we describe an execution step by step. A characterization of reachable space and a characterization of diverging states of a nondeterministic quantum program are presented. We establish a zero-one law for termination probability of the states in the reachable space. A combination of these results leads to a necessary and sufficient condition for termination of nondeterministic quantum programs. Based on this condition, an algorithm is found for checking termination of nondeterministic quantum programs within a fixed finite-dimensional state space.
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ISSN:0001-5903
1432-0525
DOI:10.1007/s00236-013-0185-3