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- W2883276125 abstract "In this thesis, we study randomized and quantumalgorithms in the query complexity model. We investigate when andby how much quantum algorithms provide a speedup over the bestpossible classical algorithm in the query complexity setting. Weintroduce a total Boolean function that exhibits a power 2.5quantum speedup compared to the best possible randomized algorithm.In the process, we introduce the method for turningpartial Boolean functions into total Boolean functions, and examinesome of its other applications. We also study lower boundtechniques for randomized algorithms. We introduce a measure calledrandomized sabotage complexity which lower bounds randomized querycomplexity and behaves well under compositions. This tool forcontrolling the randomized query complexity of composed functionscombines nicely with the cheat sheet technique, which oftenfeatures composed functions in its applications. In addition, westudy the quantum analogue of this tool, and use it to show a newpower 5 relationship between zero-error and bounded-error quantumquery complexity. Finally, we characterize the total Booleanfunctions that exhibit exponential quantum speedups when theirdomain is restricted to an arbitrarily chosen set. We show thatsuch a sculpting of a quantum speedup is possible if and only ifthe original total function has many inputs with large certificatecomplexity. Along the way, we also show that functions defined onvery small domains or that are very unbalanced can display at mosta quadratic quantum speedup." @default.
- W2883276125 created "2018-08-03" @default.
- W2883276125 creator A5088714077 @default.
- W2883276125 date "2017-01-01" @default.
- W2883276125 modified "2023-09-26" @default.
- W2883276125 title "Quantum speedups in query complexity" @default.
- W2883276125 hasPublicationYear "2017" @default.
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