Five Starter Problems: Solving Quadratic Unconstrained Binary Optimization Models on Quantum Computers

TL;DR

This tutorial introduces practical methods for solving Quadratic Unconstrained Binary Optimization models on current quantum computers, bridging theory and practice with examples, explanations, and implementation guides for both academic and industry audiences.

Contribution

It provides a comprehensive, beginner-friendly guide to applying quantum algorithms to QUBO problems using IBM and D-Wave systems, including code resources and practical insights.

Findings

Demonstrated solutions for canonical QUBO problems on quantum hardware

Provided implementation guides and code for quantum heuristics

Bridged theoretical concepts with practical quantum computing applications

Abstract

This tutorial offers a quick, hands-on introduction to solving Quadratic Unconstrained Binary Optimization (QUBO) models on currently available quantum computers and their simulators. We cover both IBM and D-Wave machines: IBM utilizes a gate-circuit architecture, and D-Wave is a quantum annealer. We provide examples of three canonical problems and two models from practical applications. The tutorial is structured to bridge the gap between theory and practice: we begin with an overview of QUBOs, explain their relevance and connection to quantum algorithms, introduce key quantum computing concepts, provide the foundations for two quantum heuristics, and provide detailed implementation guides. An associated GitHub repository provides the codes in five companion notebooks. In addition to reaching undergraduate and graduate students in computationally intensive disciplines, this article aims to reach working industry professionals seeking to explore the potential of near-term quantum applications. As our title indicates, this tutorial is intended to be a starting point in a journey towards solving more complex QUBOs on quantum computers.