Algorithms for Quantum Computers

TL;DR

This paper surveys various quantum algorithms, highlighting recent advances in quantum Fourier transforms, quantum search, quantum walks, and tensor network evaluation, illustrating the field's breadth and depth.

Contribution

It provides a comprehensive overview of recent developments in quantum algorithms, emphasizing new paradigms like quantum walks and tensor network methods.

Findings

Overview of quantum Fourier transform algorithms

Discussion of quantum search and its generalizations

Introduction to quantum walk and tensor network algorithms

Abstract

This paper surveys the field of quantum computer algorithms. It gives a taste of both the breadth and the depth of the known algorithms for quantum computers, focusing on some of the more recent results. It begins with a brief review of quantum Fourier transform based algorithms, followed by quantum searching and some of its early generalizations. It continues with a more in-depth description of two more recent developments: algorithms developed in the quantum walk paradigm, followed by tensor network evaluation algorithms (which include approximating the Tutte polynomial).