AQRC-FM: Finite-Shot Quantum Reservoir Computing with Fading Memory and Confidence-Gated Memory for Multi-Horizon Weather Forecasting and Rare-Event Assessment

Abstract: Quantum reservoir computing (QRC) is attractive for temporal prediction because the quantum dynamics are fixed and only a linear readout is trained. Whether such a reservoir helps on real meteorological data, and which of its components matter, is rarely tested against strong classical baselines under a leakage-audited protocol. We present AQRC-FM, a simulated finite-shot QRC pipeline with (i) a fading-memory input window processed by a bank of random 8-qubit Hamiltonian reservoirs with four encodings, (ii) a finite-shot observable readout, and (iii) a confidence-gated feature memory that switches to a regime-specific memory prototype when a confidence score, based on shot noise and encoding disagreement, falls below a threshold. We evaluate it on pooled ERA5/IMD/IBTRACS series for three Indian states with a purged rolling-origin protocol (test years 2023-2025, lead times 6-48 h) and an eight-check leakage audit with negative controls. AQRC-FM reaches a mean raw-unit R^2 of 0.686 (95% block-bootstrap confidence interval [0.671, 0.700]), a skill of +0.107 beyond climatology. It is competitive with, but does not outperform, strong classical models: gradient boosting (0.723), ridge regression on engineered features (0.719), and a 256-unit echo-state network (ESN, 0.706). The memory gate changes the mean R^2 by at most 0.002, which is inside the confidence intervals, so we find no measurable forecasting benefit from the gate. For rare hazards, a quantum-only readout is weak (cyclone F1 0.07, flood F1 0.03); with engineered features, AQRC-FM reaches a macro-F1 of 0.53 against 0.61 for boosting. The confidence score is associated with forecast error, and we report calibration, event-level recall, and neural-head training dynamics. We therefore position AQRC-FM as a rigorously evaluated, QRC benchmark that is competitive with, but does not outperform, strong classical baselines, and not as evidence of quantum advantage. Index Terms: echo state network, extreme-event detection, finite-shot sampling, leakage-free evaluation, quantum reservoir computing, rare-event classification, weather forecasting