Quantum‐Native Formulations for X‐Ray Fluorescence: Spectral Overlap, Sparse Elemental Identification, and Spatial Inference

ABSTRACT X‐ray fluorescence (XRF) analysis combines spectral inverse modeling, elemental support selection and spatial interpretation. We develop quadratic unconstrained binary optimization (QUBO) and Ising formulations for these tasks. A detector‐response dictionary of broadened candidate emission‐line profiles induces a spectral overlap graph that determines the coupling topology: strongly overlapping lines produce strongly coupled binary variables, providing a diagnostic of ambiguity before optimization. We formulate elemental identification using exact binary selection with physical line‐consistency penalties, derive a fixed‐point non‐negative encoding for quantized deconvolution, and express elemental‐map segmentation and trace detection as spatially regularized binary energies extending established Markov‐random‐field and detection‐limit approaches. Synchrotron low‐energy XRF combines weak fluorescence, overlapping soft X‐ray lines and large hyperspectral datacubes. The formulations are exercised on a published soft X‐ray map of THP‐1‐derived macrophages exposed to erionite fibers, acquired at the TwinMic beamline of Elettra Sincrotrone Trieste, using its detector calibration, fitted peak areas and uncertainties. The browser‐based XRFQubo demonstrator implements overlap analysis, spatial trace detection and reduced 39‐variable support selection with classical simulated annealing. Fit‐derived tests identify practical requirements for per‐line amplitude scaling, amplitude‐block moves with classical warm starts, and statistical weighting. Selection frequency broadly follows fitted peak‐area significance, while spatial regularization consolidates contiguous trace detections and suppresses isolated labels. A separate four‐qubit experiment executes restricted conditional support‐selection objectives from two measured spectra on IBM and IQM processors. No quantum advantage is claimed. Extending our companion computed tomography study, this work provides quantum‐compatible formulations and a classical demonstrator for controlled benchmarking against established XRF methods.