Quantum Search Algorithms

Abstract

This chapter reviews the general problems and the high-level operation of the major quantum algorithms. It describes some of the quantum algorithms in more detail. These algorithms include: Deutsch algorithm, Deutsch–Jozsa algorithm, Simon's algorithm, Shor's algorithm, quantum phase estimation algorithm, Grover's Quantum Search Algorithm (QSA), Boyer–Brassard–Høyer–Tapp QSA, Dürr–Høyer QSA, quantum counting algorithm, quantum heuristic algorithm, quantum genetic algorithm, Harrow–Hassidim–Lloyd algorithm, quantum mean algorithm, and quantum weighted sum algorithm. The chapter provides more physical insights into some of the algorithms. Quantum computation is based on quantum interference, which is a dynamical process that allows one to evolve initial quantum states (inputs) into final states (outputs) by modifying intermediate multi-particle superpositions in some prescribed way. The chapter illustrates how interference patterns lead to computational problems that are well suited to quantum computations, by presenting the first such problem that was proposed by David Deutsch.