Quantum algorithms for optimizers

TL;DR

This paper provides graduate-level lecture notes on quantum algorithms for optimization, covering foundational models, search, gradient methods, matrix algorithms, and adiabatic optimization, aimed at applied mathematicians and engineers.

Contribution

It offers a comprehensive, accessible introduction to quantum optimization algorithms without requiring prior quantum mechanics knowledge.

Findings

Introduces quantum search and gradient algorithms

Discusses quantum matrix manipulation techniques

Explores adiabatic optimization methods

Abstract

This is a set of lecture notes for a graduate-level course on quantum algorithms, with an emphasis on quantum optimization algorithms. It is developed for applied mathematicians and engineers, and requires no previous background in quantum mechanics. The main topics of this course, in addition to a rigorous introduction to the computational model, are: input/output models, quantum search, the quantum gradient algorithm, matrix manipulation algorithms, the mirror descent framework for semidefinite optimization (including the matrix multiplicative weights update algorithm), adiabatic optimization. This is a preprint for personal use only. Please refer to the printed version of the material.