Theory and Implementation of the Quantum Approximate Optimization Algorithm: A Comprehensible Introduction and Case Study Using Qiskit and IBM Quantum Computers

The present tutorial aims to provide a comprehensible and easily accessible introduction into the theory and implementation of the famous Quantum Approximate Optimization Algorithm (QAOA). We lay our focus on practical aspects and step-by-step guide through the realization of a proof of concept quantum application based on a real-world use case. In every step we first explain the underlying theory and subsequently provide the implementation using IBM's Qiskit. In this way we provide a thorough understanding of the mathematical modelling and the (quantum) algorithms as well as the equally important knowledge how to properly write the code implementing those theoretical concepts. As another central aspect of this tutorial we provide extensive experiments on the 27 qubits state-of-the-art quantum computer ibmq_ehningen. From the discussion of these experiments we gain an overview on the current status of quantum computers and deduce which problem sizes can meaningfully be executed on today's hardware.