Early quantum algorithms
Riccardo Manenti, Mario E. Motta · 2023
Abstract This chapter presents early quantum algorithms. We first describe Deutsch’s and Bernstein-Vazirani, some of the first quantum algorithms that showed a query advantage over their classical counterparts. We then present Grover’s algorithm, a quantum algorithm that finds an item in an unstructured database with a quadratic speed-up over classical algorithms. We explain the quantum Fourier transform, an important subroutine in various quantum algorithms. The chapter concludes with a detailed presentation of two of the most prominent applications of the quantum Fourier transform: the period finding algorithm and Shor’s algorithm for prime factorization.