Introduction to Quantum Optimization

"Quantum Natural GradientDescent"
"GradientDescent"
Follow the links for lesson notebooks

Summary

Quantum computing has the potential to address complex optimization problems that classical computers find challenging. Optimization is one of the most promising areas. It is integral to various fields, including logistics, finance, and AI. Any improvements from quantum algorithms could enhance solution quality, diversity, speed, and cost efficiency.
In the present Quantum Optimization course, we explore Variational Quantum Algorithms (VQAs), a leading framework to tackle optimization problems using today’s early-stage quantum devices. VQAs take a hybrid quantum-classical approach, using parameterized quantum circuits that learn optimal solutions through classical optimization.

Relevant Wolfram Mathematica functionalities

Out[]=
Section
Groups
Category
Items
Wolfram Mathematica
Minimization
{NMinimize,NMaximize,MinValue}
Visualization
{ContourPlot,StreamPlot}
Graphs and Networks
{Graph,VertexList,EdgeList}
Wolfram Quantum Framework
QuantumOperator & QuantumCircuitOperator
{Diagram,Table,Parameters,Matrix}
QuantumState
{Formula,StateVector,ProbabilityPlot}
Measurements
{QuantumDistance}
Quantum Optimization Paclet
Parametrized Circuits
{GenerateParameters,ParametrizedLayer,EntanglementLayer}
Gradient Methods
{GradientDescent,QuantumNaturalGradientDescent,FubiniStudyMetricTensor}
Mathematics
{QuantumLinearSolve}

Variational Quantum Eigensolver


Quantum Approximate Optimization Algorithm


Quantum Natural Gradient Descent


Variational Quantum Linear Solver


Table of contents

Lesson 1 - Introduction to Variational Quantum Algorithms (VQA)
Lesson 2 - Variational Quantum Eigensolver (VQE)
Lesson 3 - Quantum Approximate Optimization Algorithm (QAOA)
Lesson 4 - Quantum Natural Gradient Descent (QNGD)
Lesson 5 - Variational Quantum Linear Solver (VQLS)