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One of the most promising current applications of quantum computing is the simulation of quantum mechanical systems. Accurate simulations of molecular and material properties are not only fascinating from a theoretical perspective, but are also of great industrial interest. While there is currently a large focus on quantum algorithms for calculating static properties, such as energies of ground and excited states, simulations of dynamic processes have received relatively little attention.

The basic aim of this thesis is the implementation of hybrid algorithms for the simulation of molecular dynamics, in which the nuclear structure is considered classically and only the electronic structure is propagated on the quantum computer (see Ehrenfest method, Hellman-Feynman forces, etc.). After implementing known methods for model systems (e.g., Shin-Mitsu model, H2) in the first part of the thesis, new and innovative approaches will be tested and compared with already known methods. Different fermion-to-qubit mappings as well as lattice encodings in first and second quantization will be compared. In addition to a technical aptitude for these activities, a strong ability to work in a team is also expected. 

The thesis will be doubly supervised by a physicist with extensive expertise in quantum simulation of dynamical processes, who will instruct the algorithmic part of the thesis, and a chemical engineer with many years of experience in classical simulation of non-adiabatic molecular dynamics, who will be available to advise on applications. The thesis will be supervised and carried out in English.