Quantum Signal Processing for Fault-Tolerant Photonic Computing and Quantum-Enhanced Scientific Intelligence

Abstract: Quantum signal processing (QSP) provides a mathematically economical mechanism for transforming the spectral information of a block-encoded operator through carefully phased single-qubit rotations. Photonic quantum computing, meanwhile, offers high-bandwidth operation, network compatibility and substantial room-temperature functionality, yet remains constrained by optical loss, probabilistic state preparation, finite squeezing, detector imperfections and the resource overhead of logical error correction. This paper develops an integrated analytical framework that connects QSP polynomial synthesis to fault-tolerant photonic execution and to a broader construct termed quantum-enhanced scientific intelligence: the reliable extraction of predictive, explanatory and decision-relevant knowledge from complex scientific operators and data. The study adopts a theory-building and model-based research design. It combines block encoding, QSP and quantum singular-value transformation with open-system dynamics, logical-error modelling, constrained multi-objective optimization and risk-adjusted outcome scoring. The proposed QSP-FTSI framework treats algorithmic approximation error, photonic component quality, decoder performance, logical reliability, resource intensity, uncertainty calibration and scientific utility as coupled rather than independent variables. An illustrative normalized model yields a baseline benefit index of 7.942, a composite risk index of 2.640 and a risk-adjusted score of 6.358 on a ten-point scale; an improved low-loss, high-QEC scenario reaches 7.858, whereas a stressed configuration falls to 3.754. These values are demonstrations, not experimental findings. The principal contribution is a publication-ready mathematical architecture for evaluating when QSP-enabled photonic systems can support scientifically meaningful simulation, inverse modelling, spectral filtering and inference under explicit fault-tolerance and reproducibility constraints. The framework also identifies measurable pathways for experimental validation, hardware–algorithm co-design and responsible scientific deployment. Keywords quantum signal processing; quantum singular-value transformation; fault-tolerant photonic computing; block encoding; Gottesman–Kitaev–Preskill codes; fusion-based quantum computation; logical error suppression; Hamiltonian simulation; scientific machine learning; quantum-enhanced inference; photonic integrated circuits; spectral transformation; quantum error correction; risk-adjusted scientific intelligence; hardware–algorithm co-design