Background:
Quantum Computing (QC) is an emerging technology that holds the potential to revolutionise the way we will be solving computational mechanics problems in the future. The potential advantage of QC over classical high-performance computing, however, does not come for free but requires the redesign of solution approaches from scratch, that is, in terms of quantum or hybrid quantum-classical algorithms that exploit the principles of quantum mechanics such as superposition of states, entanglement, and quantum parallelism. It also requires a rethinking of the overall problem formulation as a potential computational advantage can easily get destroyed if the user aims to extract the full solution fields of, say, a quantum-CFD computation, which would require up to exponentially many computations.

Course objectives:
This advanced course provides a gentle introduction to the basic principles of quantum computing and discusses a large spectrum of quantum and hybrid quantum-classical algorithms and their applications in computational mechanics. In particular, the course will address the commonalities of and differences between gate-based quantum computers (GBQC) and quantum annealers (QA) and discuss how various problem types from the mechanical sciences can be formulated as quantum circuits for the former and Ising models (IM) / quadratic unconstrained binary optimization problems (QUBO) for the latter, respectively. The types of applications range from structural design optimization and seismic imaging to fluid and power flow analysis.

Course outline and target audience:
The course primarily addresses students and practitioners from industry and academia with backgrounds in the mechanical sciences who want to know more about the opportunities and challenges of quantum computing as an emerging computing technology to solve challenging problems in the (near) future.
The outline of the course is as follows:
- Introduction into quantum computing with discussion of the commonalities and differences of gate-based quantum computers, quantum annealers, and Ising machines.
- Formulation of QUBOs / Ising models using different encodings and approaches to implement constraints; tips and tricks for practical implementations on quantum annealers and Ising machines.
- Application of quantum annealers to solving problems in truss optimization, structural design analysis and optimization, seismic imaging, phase-field analysis, as well as fluid and power flow analysis.
- Advanced topics in quantum annealing: representation of real-valued variables, hybridization strategies, Ising machines beyond quantum annealers.
- Introduction into variational quantum algorithms (VQA) and quantum machine learning (QML) for gate-based quantum computers: quantum kernel methods (QKM), classical and quantum support vector machines (SVM).
- VQA and the Density Matrix Renormalization Group algorithm for solving the Stacking Sequence Retrieval problem with constraints.
- SVM for strength prediction of open hole composite panels.
- QKM for solving regression problems.
- QKM and physics-informed QML for solving differential equations.
- Quantum (lattice) Boltzmann methods.
- Quantum-PDE algorithms based on the finite volume/element method for CFD applications, radiation hydrodynamics, and numerical relativity.