On the quantum hardness of solving isomorphism problems as nonabelian hidden shift problems

    Authors

    A. M. Childs;P. Wocjan

    Comments

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    Abbreviated Journal Title

    Quantum Inform. Comput.

    Keywords

    quantum algorithms; hidden subgroup problem; hidden shift problem; SUBGROUP PROBLEM; ALGORITHMS; COMPUTATION; Computer Science, Theory & Methods; Physics, Particles & Fields; Physics, Mathematical

    Abstract

    We consider an approach to deciding isomorphism of rigid n-vertex graphs (and related isomorphism problems) by solving a nonabelian hidden shift problem on a quantum computer using the standard method. Such an approach is arguably more natural than viewing the problem as a hidden subgroup problem. We prove that the hidden shift approach to rigid graph isomorphism is hard in two senses. First, we prove that Omega(n) copies of the hidden shift states are necessary to solve the problem (whereas O (n log n) copies are sufficient). Second, we prove that if one is restricted to single-register measurements, an exponential number of hidden shift states are required.

    Journal Title

    Quantum Information & Computation

    Volume

    7

    Issue/Number

    5-6

    Publication Date

    1-1-2007

    Document Type

    Article

    Language

    English

    First Page

    504

    Last Page

    521

    WOS Identifier

    WOS:000248425500006

    ISSN

    1533-7146

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