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.