Abstract
In order to assess potential advantages of quantum algorithms that require quantum oracles as subroutines, the careful evaluation of the overall complexity of the oracles themselves is crucial. This study examines the quantum routines required for the implementation of oracles used in the block-encoding of the stiffness and mass matrices, which typically emerge in the finite element analysis of elastic structures. Starting from basic quantum adders, we show how to construct the necessary oracles, which require the calculation of polynomials, square root and the implementation of conditional operations. We propose quantum subroutines based on fixed-point arithmetic that, given an -qubit register, construct the oracle using ancilla qubits and have a runtime, with the order at which we truncate the polynomials,