Proxy-Based Diagnostics of Quantum Oracle Sketching Robustness for Non-IID Sensor and Telemetry Streams

Published quantum-streaming theory establishes quantum memory advantages for specific streaming problems; how a correlation-sensitive proxy model behaves under the structured dependence typical of sensor and telemetry streams, however, remains uncharted. We present a proxy-based diagnostic and hypothesis-generation framework for correlation-sensitive streaming analysis. Operational proxies for the refreshing time τ and repetition number r, introduced in this paper, are estimated on five synthetic non-IID regimes (IID, Markov switching, seasonal drift, burst repetition, and long-range dependence) and mapped onto a (τ,r) sensitivity landscape-the paper's central artifact. Three memory-bounded classical baselines (online SGD, averaged SGD, and Count-Min) supply empirical reference points; no quantum algorithm is implemented or simulated and all quantum curves are heuristic proxy estimates. Analytic and empirical refreshing-time estimates diverge by up to 125× under long-range dependence (≈8× for Markov)-the two estimators answer different questions about temporal dependence. Using empirical τ, the proxy model predicts a hypothesised proxy-favourable region under mild-to-moderate Markov correlation that closes as correlation strengthens: the mean curves cross at ρ*≈0.82 under the operating constants (C=2, δ=0.05; the crossing moves between ρ*≈0.38 and beyond the sweep range across a C-δ grid, so only the ordinal reading is robust), and by ρ=0.88 the classical baseline exceeds the proxy estimate (Hodges-Lehmann difference 0.046). Applied unchanged to two real NAB telemetry streams, the same estimators place NYC Taxi inside and Machine Temperature outside the hypothesised favourable region-an ordering that persists across all tested encoder resolutions-with imbalance-aware metrics guarding against majority-class artefacts. Ablations over the τ estimator, forward window, stream length, target function, and proxy constants preserve the regime ordering within each estimator family.