The aim of subproject B6 within the DFG Collaborative Research Centre 1375/2 NOA is to systematically formulate problems in photonics as quantum algorithms using the established framework of qubits and elementary quantum gates. Many central challenges in photonics are based on wave interference and are therefore, in principle, well suited for implementation on quantum computers, whose computational paradigm itself relies on interference processes. Accordingly, the project does not merely seek to transfer classical wave-propagation problems to quantum hardware, but explicitly aims to exploit the inherent exponential scaling potential of quantum-based computational methods.

In a first step, algorithms for non-quantized wave propagation are developed. This class of problems is theoretically well understood, particularly with respect to the underlying symmetries, which play a key role in achieving efficient formulations in terms of quantum gates. The research investigates different implementations of differential operators, Fourier-based approaches, and the modelling of matter, including arbitrarily defined material distributions, dispersion effects, and dissipative losses.

Building on these results, strategies for the efficient preparation of suitable initial states, the definition of physically meaningful observables, and the practical implementation on real quantum computing hardware are developed and tested.

The limited ability of current quantum algorithms to represent genuine nonlinearities initially restricts this approach to linear wave phenomena, with possible extensions to selected cases such as pump non-depletion and spontaneous parametric down-conversion (SPDC). The modelling of true nonlinear effects, however, requires the formulation of fully quantized electromagnetic fields. While conceptually much more demanding, this approach promises substantial scientific gains, as classical numerical methods reach their limits precisely in this regime and exponential computational advantages are required to make progress. The investigation of such fully quantized models therefore constitutes another central component of the project.