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On a class of quantum Turing machine halting deterministically

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Abstract

We consider a subclass of quantum Turing machines (QTM), named stationary rotational quantum Turing machine (SR-QTM), which halts deterministically and has deterministic tape head position. A quantum state transition diagram (QSTD) is proposed to describe SR-QTM. With QSTD, we construct a SR-QTM which is universal for all near-trivial transformations. This indicates there exists a QTM which is universal for the above subclass. Finally we show that SR-QTM is computational equivalent with ordinary QTM in the bounded error setting. It can be seen that SR-QTMs have deterministic tape head position and halt deterministically, and thus the halting scheme problem will not exist for this class of QTMs.

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Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Min Liang & Li Yang

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  1. Min Liang
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  2. Li Yang
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Correspondence to Li Yang.

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Liang, M., Yang, L. On a class of quantum Turing machine halting deterministically. Sci. China Phys. Mech. Astron. 56, 941–946 (2013). https://doi.org/10.1007/s11433-013-5048-y

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  • DOI: https://doi.org/10.1007/s11433-013-5048-y

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