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Quantum computation with write-only memory

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Abstract

In classical computation, a “write-only memory” (WOM) is little more than an oxymoron, and the addition of WOM to a (deterministic or probabilistic) classical computer brings no advantage. We prove that quantum computers that are augmented with WOM can solve problems that neither a classical computer with WOM nor a quantum computer without WOM can solve, when all other resource bounds are equal. We focus on realtime quantum finite automata, and examine the increase in their power effected by the addition of WOMs with different access modes and capacities. Some problems that are unsolvable by two-way probabilistic Turing machines using sublogarithmic amounts of read/write memory are shown to be solvable by these enhanced automata.

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Notes

  1. The QTM model is appropriate for studying the effect of space bounds on computational power. See Yao (1993) for an alternative model of quantum computation.

  2. Unlike Watrous (1998), we also allow efficiently computable irrational numbers as transition amplitudes in our QTM’s. This simplifies the description of some algorithms in the remainder of this paper.

  3. The reader may find it useful to consult the descriptions of the common notational items in the discussion, given immediately after the introduction.

  4. Note that our definition of quantum counter automata is more general than the previous ones (Kravtsev 1999; Bonner et al. 2001; Yamasaki et al. 2002, 2005), since it is based on general quantum operators.

  5. Note that each transition of \({\mathcal{M}}\) in Eq. 1 writes a symbol determined by the source state of the corresponding transition of \({\mathcal{D}}\) to the register. This ensures the orthonormality condition for quantum machines described earlier.

  6. This idea has been adapted from an algorithm by Kondacs and Watrous for a different type of quantum automaton, whose analysis can be found in Kondacs and Watrous (1997).

  7. RT-N1BCAs can also recognize \(L_{center} = \{ ubv \mid u,v \in \{a,b\}^{*},|u|=|v| \},\) and the languages studied in (Freivalds et al. 2010), none of which can be recognized by RT-QFAs with unbounded error.

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Acknowledgments

Yakaryılmaz and Say were partially supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) with grant 108E142. Freivalds and Agadzanyan were partially supported by Grant No. 09.1570 from the Latvian Council of Science and by Project 2009/0216/1DP/1.1.2.1.2/09/IPIA /VIA/004 from the European Social Fund.

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Authors and Affiliations

  1. Department of Computer Engineering, Boğaziçi University, Bebek, 34342, İstanbul, Turkey

    Abuzer Yakaryılmaz & A. C. Cem Say

  2. Institute of Mathematics and Computer Science, University of Latvia, Raiņa Bulvāris 29, Riga, LV-1459, Latvia

    Rūsiņš Freivalds & Ruben Agadzanyan

Authors
  1. Abuzer Yakaryılmaz
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  2. Rūsiņš Freivalds
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  3. A. C. Cem Say
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  4. Ruben Agadzanyan
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Correspondence to Abuzer Yakaryılmaz.

Additional information

This paper is an extended version of some of the material in (A. Yakaryılmaz, R. Freivalds, A. C. C. Say, and R. Agadzanyan. Quantum computation with devices whose contents are never read. In Unconventional Computation, volume 6079 of LNCS, pages 164–174, 2010), presented in the 9th International Conference on Unconventional Computation (UC2010).

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Yakaryılmaz, A., Freivalds, R., Say, A.C.C. et al. Quantum computation with write-only memory. Nat Comput 11, 81–94 (2012). https://doi.org/10.1007/s11047-011-9270-0

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