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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References
Deutsch D. Quantum-theory, the church-Turing principle and the universal quantum computer. Proc R Soc Lond A, 1985, 400(1818): 97–117
Myers JM. Can a universal quantum computer be fully quantum? Phys Rev Lett, 1997, 78(9): 1823–1824
Ozawa M. Quantum nondemolition monitoring of universal quantum computers. Phys Rev Lett, 1998, 80(3): 631–634
Linden N, Popescu S. The halting problem for quantum computers. arXiv:quant-ph/9806054
Ozawa M. Halting of quantum Turing machines. In: Calude C S, ed. Unconventional Models of Computation. Berlin: Springer-Verlag, 2002. LNCS 2509: 58-65
Kieu T, Danos M. A no-go theorem for halting a universal quantum computer. Physica A, 2001, 14(1): 217–225
Shi Y. Remarks on universal quantum computer. Phys Lett A, 2002, 293(5–6): 277–282
Fouche W, Heidema J, Jones G, et al. Halting in quantum Turing computation. In: Adamatzky A, Bull L, Costello B, et al., eds. Unconventional Computing 2007. Bristol: Luniver Press, 2007. 101–112
Bernstein E, Vazirani U. Quantum complexity theory. SIAMJ Comput, 1997, 26(5): 1411–1473
Miyadera T, Ohya M. On halting process of quantum turing machine. Open Syst Inf Dyn, 2005, 12(3): 261–264
Liang M, Yang L. Universal quantum circuit of near-trivial transformations. Sci China-Phys Mech Astron, 2011, 54(10): 1819–1827
Watrous J. On one-dimensional quantum cellular automata. In: Proceedings of the 36th Annual Symposium on Foundations of Computer Science. Milwaukee: IEEE, 1995. 528–537
Hook L R I, Lee S C. Quantum state transition diagrams-a bridge from classical computing to quantum computing. Proc SPIE, 2010, 7646: 76460R
Barenco A, Bennett C, Cleve R, et al. Elementary gates for quantum computation. Phys Rev A, 1995, 52(5): 3457–3467
Nielsen M, Chuang I. Quantum Computation and Quantum Information. England: Cambridge University Press, 2000. 175–176
Bera D, Fenner S, Green F, et al. Universal quantum circuits. arXiv:0804.2429
Nishimura H, Ozawa M. Computational complexity of uniform quantum circuit families and quantum Turing machines. Theor Comput Sci, 2002, 276(1-2): 147–181
Yao A. Quantum circuit complexity. In: Proceedings of the 34th Annual Symposium on Foundations of Computer Science. Palo Alto: IEEE, 1993. 352–361
Nishimura H, Ozawa M. Perfect computational equivalence between quantum Turing machines and finitely generated uniform quantum circuit families. Quantum Inf Proc, 2009, 8(1): 13–24
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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