Acta Informatica

, Volume 51, Issue 1, pp 1–24

Termination of nondeterministic quantum programs

Original Article

DOI: 10.1007/s00236-013-0185-3

Cite this article as:
Li, Y., Yu, N. & Ying, M. Acta Informatica (2014) 51: 1. doi:10.1007/s00236-013-0185-3


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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Tsinghua National Laboratory of Information Science and Technology, Department of Computer Science and TechnologyTsinghua UniversityBeijingChina
  2. 2.Center for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information TechnologyUniversity of TechnologySydneyAustralia

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