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Termination of nondeterministic quantum programs

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Abstract

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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Acknowledgments

We are grateful to Runyao Duan and Yuan Feng for useful discussions. This work was partly supported by the Australian Research Council (Grant No: DP110103473) and the National Natural Science Foundation of China (Grant No: 60736011).

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Authors and Affiliations

  1. Tsinghua National Laboratory of Information Science and Technology, Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, China

    Yangjia Li & Nengkun Yu

  2. Center for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology, Sydney, NSW, 2007, Australia

    Mingsheng Ying

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  1. Yangjia Li
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  2. Nengkun Yu
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  3. Mingsheng Ying
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Correspondence to Yangjia Li.

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Li, Y., Yu, N. & Ying, M. Termination of nondeterministic quantum programs. Acta Informatica 51, 1–24 (2014). https://doi.org/10.1007/s00236-013-0185-3

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  • DOI: https://doi.org/10.1007/s00236-013-0185-3

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