Quantum Optimization with IBM Quantum (openHPI)

A practical course on using quantum computers to tackle combinatorial optimization problems, developed by the Hasso Plattner Institute in collaboration with IBM Quantum. Free and self-paced on the openHPI platform, the course focuses on the Quantum Approximate Optimization Algorithm (QAOA) and the Variational Quantum Eigensolver (VQE), the leading near-term approaches to quantum optimization.

Optimization is one of the most commercially significant potential application areas for quantum computing, spanning logistics, finance, drug discovery, and supply chain management. This course gives you the tools to formulate and run quantum optimization experiments using Qiskit.

What you’ll learn

• Combinatorial optimization fundamentals: the types of optimization problems quantum computers target, NP-hard problems, and why combinatorial optimization is hard for classical computers
• Quadratic unconstrained binary optimization (QUBO): how to reformulate classical optimization problems as QUBO instances, which is the standard input format for quantum optimization algorithms
• The Ising model: the mapping from QUBO to the Ising Hamiltonian that quantum hardware can represent, and why this mapping is central to quantum optimization
• The Variational Quantum Eigensolver (VQE): parameterized ansatz circuits, the variational principle, the hybrid classical-quantum training loop, and how VQE finds ground state energies
• The Quantum Approximate Optimization Algorithm (QAOA): the QAOA circuit structure using problem and mixer Hamiltonians, the p-layer depth parameter, and the relationship between approximation quality and circuit depth
• Practical Qiskit implementation: Qiskit’s optimization module, defining QUBO problems, constructing QAOA circuits, and running experiments on simulators
• Limitations and realism: honest assessment of where QAOA provides advantage over classical heuristics today, and what the research literature says

Course structure

The course builds from optimization problem formulation through QUBO and Ising model representations, then introduces VQE and QAOA with full Qiskit implementations. Graded programming assignments reinforce each topic, and a Record of Achievement is available for learners who meet the minimum score threshold.

Who is this for?

• Operations researchers and data scientists who want to understand quantum optimization and assess its relevance to their work
• Quantum computing students looking to move from algorithms theory to near-term application domains
• Developers working in logistics, finance, or scheduling who want to experiment with quantum approaches to optimization
• Anyone who has heard about QAOA and wants to actually implement and run it

Prerequisites

Familiarity with quantum computing basics and Qiskit is recommended. The openHPI “Introduction to Quantum Computing with Qiskit” course is good preparation. Basic familiarity with optimization concepts (objective functions, constraints) is helpful. Python programming experience is needed for the coding exercises.

Hands-on practice

Exercises use Qiskit and its optimization extensions:

• Formulate the Max-Cut problem as a QUBO instance and map it to an Ising Hamiltonian
• Build and run a QAOA circuit for Max-Cut at varying circuit depths (p=1, p=2, p=3) and compare approximation quality
• Implement VQE for a small Ising problem and verify the result against exact diagonalization
• Use Qiskit’s optimization module to define a custom QUBO problem and solve it with QAOA
• Analyse how solution quality changes with the number of optimization iterations

Why take this course?

Quantum optimization is one of the most actively debated application areas in quantum computing, with significant commercial interest and ongoing research into whether QAOA can outperform classical heuristics. This course gives you the technical foundation to follow that debate intelligently and to run your own experiments.

The IBM Quantum collaboration ensures the Qiskit implementation is accurate and current. The honest treatment of limitations is refreshing: rather than overselling near-term quantum optimization, the course gives you the tools to evaluate claims critically and to run experiments that let the hardware speak for itself.