Evaluation of Pulse Level Quantum Fourier Models

The promising field of Quantum Machine Learning (QML) widely employs Parametrized Quantum Circuits (PQCs). Specifically, PQCs whose output can be represented as a truncated Fourier series are often referred to as Quantum Fourier Models (QFMs). Using this representation enables the analysis through spectral properties, providing insights into the capability of PQCs to learn patterns in data. Typically, QFMs in this research area are conceptualized and implemented using gates, which serve as mathematical abstractions of quantum mechanical operations. This work moves beyond this abstract gate-level description by investigating if and how QFMs can be directly modeled at the pulse-level. This approach more accurately reflects the physical reality of quantum hardware, where gates are realized as electromagnetic pulses. The thesis at hand is concerned with both, theoretically derived and numerically validated framework, for constructing QFMs at the pulse-level. The provided framework grants increased control, due to the direct manipulation of pulse parameters, thereby laying a solid foundation for further investigations into the theoretical properties of QFMs.