{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T09:07:25Z","timestamp":1788858445318,"version":"build-2803163510"},"reference-count":54,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2026,9,4]],"date-time":"2026-09-04T00:00:00Z","timestamp":1788480000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>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 \u03c4 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 (\u03c4,r) sensitivity landscape\u2014the paper\u2019s 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\u00d7 under long-range dependence (\u22488\u00d7 for Markov)\u2014the two estimators answer different questions about temporal dependence. Using empirical \u03c4, 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 \u03c1*\u22480.82 under the operating constants (C=2, \u03b4=0.05; the crossing moves between \u03c1*\u22480.38 and beyond the sweep range across a C\u2013\u03b4 grid, so only the ordinal reading is robust), and by \u03c1=0.88 the classical baseline exceeds the proxy estimate (Hodges\u2013Lehmann 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\u2014an ordering that persists across all tested encoder resolutions\u2014with imbalance-aware metrics guarding against majority-class artefacts. Ablations over the \u03c4 estimator, forward window, stream length, target function, and proxy constants preserve the regime ordering within each estimator family.<\/jats:p>","DOI":"10.3390\/s26175629","type":"journal-article","created":{"date-parts":[[2026,9,4]],"date-time":"2026-09-04T17:25:56Z","timestamp":1788542756000},"page":"5629","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Proxy-Based Diagnostics of Quantum Oracle Sketching Robustness for Non-IID Sensor and Telemetry Streams"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-2574-6533","authenticated-orcid":false,"given":"Mohammed","family":"Farsi","sequence":"first","affiliation":[{"name":"Computer Information Systems Department, Taibah University, Yanbu 46477, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0618-5662","authenticated-orcid":false,"given":"Muhammad","family":"Mahmoud","sequence":"additional","affiliation":[{"name":"Information Systems Department, Faculty of Computers and Artificial Intelligence, Matrouh University, Matrouh 51511, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"software","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5996-6019","authenticated-orcid":false,"given":"Abdelmoniem","family":"Helmy","sequence":"additional","affiliation":[{"name":"Computer Information Systems Department, Taibah University, Yanbu 46477, Saudi Arabia"},{"name":"Department of Information Systems and Technology, Faculty of Graduate Studies for Statistical Research, Cairo University, Cairo 12613, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1561\/0400000002","article-title":"Data streams: Algorithms and applications","volume":"1","author":"Muthukrishnan","year":"2005","journal-title":"Found. Trends Theor. Comput. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1006\/jcss.1997.1545","article-title":"The space complexity of approximating the frequency moments","volume":"58","author":"Alon","year":"1999","journal-title":"J. Comput. Syst. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/90.282603","article-title":"On the self-similar nature of Ethernet traffic (extended version)","volume":"2","author":"Leland","year":"1994","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1109\/90.554723","article-title":"Self-similarity through high-variability: Statistical analysis of Ethernet LAN traffic at the source level","volume":"5","author":"Willinger","year":"1997","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"e1536","DOI":"10.1002\/widm.1536","article-title":"A systematic review on detection and adaptation of concept drift in streaming data using machine learning techniques","volume":"14","author":"Arora","year":"2024","journal-title":"WIREs Data Min. Knowl. Discov."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1145\/2523813","article-title":"A survey on concept drift adaptation","volume":"46","author":"Gama","year":"2014","journal-title":"ACM Comput. Surv."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"120799","DOI":"10.1016\/j.ins.2024.120799","article-title":"Elastic online deep learning for dynamic streaming data","volume":"676","author":"Su","year":"2024","journal-title":"Inf. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"120796","DOI":"10.1016\/j.ins.2024.120796","article-title":"Online learning for data streams with bi-dynamic distributions","volume":"676","author":"Yan","year":"2024","journal-title":"Inf. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Kallaugher, J. (2022, January 7\u201310). A quantum advantage for a natural streaming problem. Proceedings of the 62nd IEEE Annual Symposium on Foundations of Computer Science (FOCS), Denver, CO, USA.","DOI":"10.2172\/2001507"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Kallaugher, J., Parekh, O., and Voronova, N. (2025, January 13\u201315). How to design a quantum streaming algorithm without knowing anything about quantum computing. Proceedings of the 2025 Symposium on Simplicity in Algorithms (SOSA), New Orleans, LA, USA.","DOI":"10.1137\/1.9781611978315.2"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Kallaugher, J., Parekh, O., and Voronova, N. (2024, January 24\u201328). Exponential quantum space advantage for approximating maximum directed cut in the streaming model. Proceedings of the 56th Annual ACM Symposium on Theory of Computing (STOC), Vancouver, BC, Canada.","DOI":"10.1145\/3618260.3649709"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1038\/nphys3272","article-title":"Read the fine print","volume":"11","author":"Aaronson","year":"2015","journal-title":"Nat. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2631","DOI":"10.1038\/s41467-021-22539-9","article-title":"Power of data in quantum machine learning","volume":"12","author":"Huang","year":"2021","journal-title":"Nat. Commun."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Tang, E. (2019, January 23\u201326). A quantum-inspired classical algorithm for recommendation systems. Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, Phoenix, AZ, USA.","DOI":"10.1145\/3313276.3316310"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"150502","DOI":"10.1103\/PhysRevLett.103.150502","article-title":"Quantum algorithm for linear systems of equations","volume":"103","author":"Harrow","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1038\/s41586-019-0980-2","article-title":"Supervised learning with quantum-enhanced feature spaces","volume":"567","author":"Temme","year":"2019","journal-title":"Nature"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"032430","DOI":"10.1103\/PhysRevA.103.032430","article-title":"Effect of data encoding on the expressive power of variational quantum-machine-learning models","volume":"103","author":"Schuld","year":"2021","journal-title":"Phys. Rev. A"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1038\/nature23474","article-title":"Quantum machine learning","volume":"549","author":"Biamonte","year":"2017","journal-title":"Nature"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1038\/s42254-021-00348-9","article-title":"Variational quantum algorithms","volume":"3","author":"Cerezo","year":"2021","journal-title":"Nat. Rev. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"79","DOI":"10.22331\/q-2018-08-06-79","article-title":"Quantum computing in the NISQ era and beyond","volume":"2","author":"Preskill","year":"2018","journal-title":"Quantum"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Schuld, M., and Petruccione, F. (2018). Supervised Learning with Quantum Computers. Quantum Science and Technology, Springer.","DOI":"10.1007\/978-3-319-96424-9"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1050","DOI":"10.1038\/s41567-020-0932-7","article-title":"Predicting many properties of a quantum system from very few measurements","volume":"16","author":"Huang","year":"2020","journal-title":"Nat. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.jalgor.2003.12.001","article-title":"An improved data stream summary: The count-min sketch and its applications","volume":"55","author":"Cormode","year":"2005","journal-title":"J. Algorithms"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1762","DOI":"10.1137\/15M1009718","article-title":"Frequent directions: Simple and deterministic matrix sketching","volume":"45","author":"Ghashami","year":"2016","journal-title":"SIAM J. Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1561\/0400000060","article-title":"Sketching as a tool for numerical linear algebra","volume":"10","author":"Woodruff","year":"2014","journal-title":"Found. Trends Theor. Comput. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1561\/2200000018","article-title":"Online learning and online convex optimization","volume":"4","year":"2012","journal-title":"Found. Trends Mach. Learn."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"838","DOI":"10.1137\/0330046","article-title":"Acceleration of stochastic approximation by averaging","volume":"30","author":"Polyak","year":"1992","journal-title":"SIAM J. Control Optim."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Weinberger, K., Dasgupta, A., Langford, J., Smola, A., and Attenberg, J. (2009, January 14\u201318). Feature hashing for large scale multitask learning. Proceedings of the 26th International Conference on Machine Learning (ICML), Montreal, QC, Canada.","DOI":"10.1145\/1553374.1553516"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1109\/MCI.2015.2471196","article-title":"Learning in nonstationary environments: A survey","volume":"10","author":"Ditzler","year":"2015","journal-title":"IEEE Comput. Intell. Mag."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Bifet, A., and Gavald\u00e0, R. (2007, January 26\u201328). Learning from time-changing data with adaptive windowing. Proceedings of the 2007 SIAM International Conference on Data Mining, Minneapolis, MN, USA.","DOI":"10.1137\/1.9781611972771.42"},{"key":"ref_31","first-page":"1601","article-title":"MOA: Massive online analysis","volume":"11","author":"Bifet","year":"2010","journal-title":"J. Mach. Learn. Res."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.neucom.2021.04.112","article-title":"Online learning: A comprehensive survey","volume":"459","author":"Hoi","year":"2021","journal-title":"Neurocomputing"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Gama, J. (2010). Knowledge Discovery from Data Streams, Chapman & Hall\/CRC.","DOI":"10.1201\/EBK1439826119"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1469","DOI":"10.1007\/s10994-017-5642-8","article-title":"Adaptive random forests for evolving data stream classification","volume":"106","author":"Gomes","year":"2017","journal-title":"Mach. Learn."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"120979","DOI":"10.1016\/j.ins.2024.120979","article-title":"Learning evolving prototypes for imbalanced data stream classification with limited labels","volume":"679","author":"Wu","year":"2024","journal-title":"Inf. Sci."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1227","DOI":"10.1287\/opre.2015.1408","article-title":"Non-stationary stochastic optimization","volume":"63","author":"Besbes","year":"2015","journal-title":"Oper. Res."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1007\/s10994-009-5152-4","article-title":"A theory of learning from different domains","volume":"79","author":"Blitzer","year":"2010","journal-title":"Mach. Learn."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"109315","DOI":"10.1016\/j.comnet.2022.109315","article-title":"Analyzing count-min sketch with conservative updates","volume":"217","author":"Alouf","year":"2022","journal-title":"Comput. Netw."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1561\/1900000004","article-title":"Synopses for massive data: Samples, histograms, wavelets, sketches","volume":"4","author":"Cormode","year":"2011","journal-title":"Found. Trends Databases"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Park, K., and Willinger, W. (2000). Self-Similar Network Traffic and Performance Evaluation, Wiley-Interscience.","DOI":"10.1002\/047120644X"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"130503","DOI":"10.1103\/PhysRevLett.113.130503","article-title":"Quantum support vector machine for big data classification","volume":"113","author":"Rebentrost","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1038\/nphys3029","article-title":"Quantum principal component analysis","volume":"10","author":"Lloyd","year":"2014","journal-title":"Nat. Phys."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Gily\u00e9n, A., Su, Y., Low, G.H., and Wiebe, N. (2019, January 23\u201326). Quantum singular value transformation and beyond: Exponential improvements for quantum matrix arithmetics. Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, Phoenix, AZ, USA.","DOI":"10.1145\/3313276.3316366"},{"key":"ref_44","unstructured":"Chakraborty, S., Gily\u00e9n, A., and Jeffery, S. (2019, January 9\u201312). The power of block-encoded matrix powers: Improved regression techniques via faster Hamiltonian simulation. Proceedings of the 46th International Colloquium on Automata, Languages, and Programming (ICALP), Patras, Greece."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"160501","DOI":"10.1103\/PhysRevLett.100.160501","article-title":"Quantum random access memory","volume":"100","author":"Giovannetti","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"2312121","DOI":"10.1080\/09540091.2024.2312121","article-title":"Design and analysis of quantum machine learning: A survey","volume":"36","author":"Chen","year":"2024","journal-title":"Connect. Sci."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1182","DOI":"10.1126\/science.abn7293","article-title":"Quantum advantage in learning from experiments","volume":"376","author":"Huang","year":"2022","journal-title":"Science"},{"key":"ref_48","first-page":"1","article-title":"Optimal quantum sample complexity of learning algorithms","volume":"19","author":"Arunachalam","year":"2018","journal-title":"J. Mach. Learn. Res."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Levin, D.A., and Peres, Y. (2017). Markov Chains and Mixing Times, American Mathematical Society. [2nd ed.].","DOI":"10.1090\/mbk\/107"},{"key":"ref_50","unstructured":"Beran, J. (1994). Statistics for Long-Memory Processes, Chapman & Hall\/CRC."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1137\/1010093","article-title":"Fractional Brownian motions, fractional noises and applications","volume":"10","author":"Mandelbrot","year":"1968","journal-title":"SIAM Rev."},{"key":"ref_52","first-page":"473","article-title":"Practical Markov chain Monte Carlo","volume":"7","author":"Geyer","year":"1992","journal-title":"Stat. Sci."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1109\/PROC.1966.4567","article-title":"The spectrum of clipped noise","volume":"54","author":"Middleton","year":"1966","journal-title":"Proc. IEEE"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.neucom.2017.04.070","article-title":"Unsupervised real-time anomaly detection for streaming data","volume":"262","author":"Ahmad","year":"2017","journal-title":"Neurocomputing"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/17\/5629\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T08:12:46Z","timestamp":1788855166000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/17\/5629"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,4]]},"references-count":54,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2026,9]]}},"alternative-id":["s26175629"],"URL":"https:\/\/doi.org\/10.3390\/s26175629","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,4]]}}}