Mathematical Treatment and Appendices for: Integration of a Quantum Phase Estimation Algorithm to Improve the Calculation of Local Frequency Response Functions of Arbitrary Geometries for Milling Dynamics Simulation

This paper provides mathematical details and rigorous derivations for the results presented in [2]. This includes a mathematical derivation of the generalized frequency response function (FRF) for non-diagonal mass matrices and the generalization of the block encoding to matrices with arbitrary sparsity properties. Furthermore, the paper provides pseudocode for the hybrid implementation of the diagonalization step[1]. Finally, an error model extending the one from [1] to the generalized FRF is rigorously derived.