A Necessary Condition for Quantum Adiabaticity Applied to the Adiabatic Grover Search

Oleg Lychkovskiy

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)

    Abstract

    Numerous sufficient conditions for adiabaticity of the evolution of a driven quantum system have been known for quite a long time. In contrast, necessary adiabatic conditions are scarce. Recently a practicable necessary condition well suited for many-body systems has been proved. Here we tailor this condition for estimating run times of adiabatic quantum algorithms. As an illustration, the condition is applied to the adiabatic algorithm for searching in an unstructured database (adiabatic Grover search algorithm). We find that the thus obtained lower bound on the run time of this algorithm reproduces N scaling (with N being the number of database entries) of the explicitly known optimum run time. This is in contrast to the poor performance of the known sufficient adiabatic conditions, which guarantee adiabaticity only for a run time on the order of O(N), which does not constitute any speedup over the classical database search. This observation highlights the merits of the new adiabatic condition and its potential relevance to adiabatic quantum computing.

    Original languageEnglish
    Pages (from-to)552-557
    Number of pages6
    JournalJournal of Russian Laser Research
    Volume39
    Issue number6
    DOIs
    Publication statusPublished - 1 Nov 2018

    Keywords

    • adiabatic conditions
    • adiabatic Grover search
    • adiabatic quantum algorithms
    • quantum adiabatic theorem

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