The pile-up rejection in nuclear spectroscopy has been confronted recently by several pile-up correction schemes that compensate for distortions of the signal and subsequent energy spectra artifacts as the counting rate increases. We study here a real-time capability of the event-by-event correction method, which at the core translates to solving many sets of linear equations. Tight time limits and constrained front-end electronics resources make well-known direct solvers inappropriate. We propose a novel approach based on the Gauss-Seidel iterative method, which turns out to be a stable and cost-efficient solution to improve spectroscopic resolution in the front-end electronics. We show the method convergence properties for a class of matrices that emerge in calorimetric processing of scintillation detector signals and demonstrate the ability of the method to support the relevant resolutions. The sole iteration-based error component can be brought below the sliding window induced errors in a reasonable number of iteration steps, thus allowing real-time operation. An area-efficient hardware implementation is proposed that fully utilizes the method's inherent parallelism.

Modelling of electromagnetic wave propagation in telecommunications has evolved from empirical models to highly deterministic ray tracing and numerical methods. The extraordinary computational effort of these methods and their wave nature seem ideally suited to be approached by quantum algorithms. We first examine current progress by reviewing recent proposals in the field. We scrutinize potentially advantageous quantum architectures, ranging from mainstream gate-level computers and near-term, mid-scale noisy architectures with limited capabilities, to adiabatic and annealing approaches that are already in commercial use. We analyze the weaknesses and strengths of recent proposals. Beyond the core algorithm, mechanisms to bridge the quantum and classical worlds are of particular interest. Extremely diverse algorithm specifications, from those based on Hamiltonian simulations and emulation of variational optimization to the unconstrained binary formulation, are compared with the use of pure gate-level circuits and known quantum subroutines. We show that the graph Laplacian, given its ability to integrate boundary conditions, is uniquely suited for quantum propagation modelling algorithms rooted in differential numerical methods. Quantum computers could overcome the temporal and spatial limitations of classical methods for larger computational domains and, to some extent, address the problems of dispersion and stability in finite-difference approximations. The ability to express the solution of a problem as an eigenvalue problem turns out to be an advantage in the quantum world, where eigenvalues and eigenvectors are inextricably intertwined with quantum mechanics. In this paper, we identify the most promising techniques and scenarios that hold the greatest potential.