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This chapter provides concrete examples of quantum algorithms demonstrating exponential speedups compared to classical counterparts, emphasizing complexity class separations and the potential of quantum computing. Each algorithm is presented step-by-step to analyze the speedup. The Abelian Hidden Subgroup Problem is introduced as a unifying framework for exponential speedup, of which Simon’s problem is shown to be an instance.

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Simon’s, Deutsch–Jozsa, and Bernstein–Vazirani Algorithms

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  • 发表日期：

    2026年

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  • Osama M. Raisuddin,
  • Suvranu De

摘要

This chapter provides concrete examples of quantum algorithms demonstrating exponential speedups compared to classical counterparts, emphasizing complexity class separations and the potential of quantum computing. Each algorithm is presented step-by-step to analyze the speedup. The Abelian Hidden Subgroup Problem is introduced as a unifying framework for exponential speedup, of which Simon’s problem is shown to be an instance.