The Variational Quantum Eigensolver (VQE) [1] is considered as one of the most promising algorithms for near-term applications on Noisy Intermediate-Scale Quantum (NISQ) devices. It is a hybrid algorithm which uses the variational Rayleigh-Ritz principle to find the ground state energy of a quantum mechanical system and is expected to be useful for a broad range of problems in various fields, ranging from condensed matter physics over quantum chemistry to optimization [2,3,4]. Although VQE has shown some resilience to noise from quantum hardware [2], noise is one of the main obstacles on the way to its application in practical use cases. Our work focuses on a systematic investigation of the effect of quantum noise on the performance of VQE on the example of the H2 molecule.

Enhancing classical solutions for optimization problems with quantum-assisted methods proves to be difficult. It is unclear which algorithms are suited for which problems and how to implement them in a real-world setting. Mathematical formulation, encoding, decomposition and the selection of a hybrid algorithm and its hyperparameters require a vast amount of expert knowledge from many disciplines including physics, computer science, mathematics and engineering. Good, reliable solution paths need to be found and automated to lower the obstacles for end users to apply hybrid quantum-classical methods.

The Munich Quantum Valley develops different quantum computing demonstrators including the software stack up to the application. Indeed, looking early at potential applications of quantum computers can help us to understand for which kind of use cases quantum computing is promising in perspective. Furthermore, this perspective allows us to formulate requirements towards the quantum computing hardware to be built as well as towards the software stack, including the integration of HPC systems and quantum computers.