A PROMISEBQP-COMPLETE STRING REWRITING PROBLEM

    Authors

    D. Janzing;P. Wocjan

    Comments

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    Abbreviated Journal Title

    Quantum Inform. Comput.

    Keywords

    PromiseBQP; PromiseBQP-complete problems; QUANTUM ALGORITHMS; COMPUTERS; SYSTEMS; Computer Science, Theory & Methods; Physics, Particles & Fields; Physics, Mathematical

    Abstract

    We consider the following combinatorial problem. We are given three strings s, t, and t' of length L over some fixed finite alphabet and an integer in that is polylogarithmic in L. We have a symmetric relation on substrings of constant length that specifies which substrings are allowed to be replaced with each other. Let Delta(n) denote the difference between the numbers of possibilities to obtain t from s and t' from s after n is an element of N replacements. The problem is to determine the sign of A(m). As promises we have a gap condition and a growth condition. The former states that Delta(m) > = is an element of c(m) where is inverse polylogarithmic in L and c > 0 is a constant. The latter is given by Delta(n) < = c(n) for all n. We show that this problem is PromiseBQP-complete, i.e., it represents the class of problems that can be solved efficiently on a quantum computer.

    Journal Title

    Quantum Information & Computation

    Volume

    10

    Issue/Number

    3-4

    Publication Date

    1-1-2010

    Document Type

    Article

    Language

    English

    First Page

    234

    Last Page

    257

    WOS Identifier

    WOS:000276214700005

    ISSN

    1533-7146

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