{"data":{"id":"10.5281/zenodo.17910992","type":"dois","attributes":{"doi":"10.5281/zenodo.17910992","prefix":"10.5281","suffix":"zenodo.17910992","identifiers":[{"identifier":"oai:zenodo.org:17910992","identifierType":"oai"},{"identifier":"https://github.com/QDaria/qrc","identifierType":"URL"}],"alternateIdentifiers":[{"alternateIdentifierType":"oai","alternateIdentifier":"oai:zenodo.org:17910992"},{"alternateIdentifierType":"URL","alternateIdentifier":"https://github.com/QDaria/qrc"}],"creators":[{"name":"Houshmand, Daniel Mo","nameType":"Personal","givenName":"Daniel Mo","familyName":"Houshmand","affiliation":["QDaria - Quantum Machine Learning Research Consortium, Oslo, Norway"],"nameIdentifiers":[{"nameIdentifier":"0009-0008-2270-5454","nameIdentifierScheme":"ORCID"}]},{"name":"Houshmand, Daniel Mo","nameType":"Personal","givenName":"Daniel Mo","familyName":"Houshmand","affiliation":["QDaria"],"nameIdentifiers":[{"nameIdentifier":"0009-0008-2270-5454","nameIdentifierScheme":"ORCID"}]}],"titles":[{"title":"Sample Efficiency Crisis in Quantum Reservoir Computing: Scaling Analysis on 156-Qubit IBM Hardware and Rigetti Simulation"}],"publisher":"Zenodo","container":{},"publicationYear":2025,"subjects":[{"subject":"quantum reservoir computing"},{"subject":"sample efficiency"},{"subject":"NISQ"},{"subject":"IBM Heron"},{"subject":"Rigetti Novera"},{"subject":"quantum machine learning"}],"contributors":[],"dates":[{"date":"2025-12-12","dateType":"Issued"},{"date":"2025-12-12","dateType":"Created","dateInformation":"Preprint release  "}],"language":"en","types":{"ris":"GEN","bibtex":"misc","citeproc":"article","schemaOrg":"CreativeWork","resourceType":"","resourceTypeGeneral":"Preprint"},"relatedIdentifiers":[{"relationType":"IsSupplementTo","relatedIdentifier":"https://github.com/QDaria/qrc","resourceTypeGeneral":"Preprint","relatedIdentifierType":"URL"},{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.17899072","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":"1.0.0","rightsList":[{"rights":"Creative Commons Attribution 4.0 International","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rightsIdentifier":"cc-by-4.0","rightsIdentifierScheme":"SPDX"}],"descriptions":[{"description":"Abstract—We present the largest quantum reservoir computing (QRC) demonstration on real quantum hardware to date, comparing 4-qubit and 156-qubit experimental IBM systems (Heronr3) alongside high-fidelity 9-qubit Rigetti simulation employing the Steinegger-R¨ ath (2025) feature engineering methodology. On time-evolving spectral data, we achieve R2 = 0.764 (4Q, 50 samples) and R2 = 0.723 (156Q, 200 samples), surpassing previous experimental demonstrations of 120 qubits [1] and 108 qubits [2]. To validate QRC generalizability across chaotic regimes, we demonstrate multi-system validation on canonical chaotic attractors: Lorenz-63 (R2 = 0.796, λ = 0.906) and Rossler (R2 = 0.969, λ = 0.071), achieving average R2 = 0.908 across systems spanning a 13× range in Lyapunov exponents. While these results validate QRC methodology on complex dynamics, direct comparison reveals sample efficiency challenges: the 156-qubit system operates at 1.28 samples/feature versus 5.0 for 4Q. Meanwhile, simulated 9-qubit Rigetti Novera achieves R2 = 0.959 on the same spectral evolution data through polynomial feature engineering (3,375 features, 0.19 samples/feature with ridge regularization), demonstrating that sophisticated readout strategies can overcome data quality limitations. We identify optimal qubit counts of 8-16 for current data availability and provide the first validation of QRC on 156-qubit NISQ hardware, with implications for quantum machine learning resource allocation. Index Terms—Quantum reservoir computing, sample efficiency, turbulence forecasting, NISQ devices, feature engineering, hardware scaling, quantum machine learning, IBM Heron, Rigetti Novera","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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","url":"https://zenodo.org/doi/10.5281/zenodo.17910992","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"viewsOverTime":[],"downloadCount":0,"downloadsOverTime":[],"referenceCount":0,"citationCount":0,"citationsOverTime":[{"year":"2025","total":1}],"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":1,"created":"2025-12-12T12:21:19.000Z","registered":"2025-12-12T12:21:20.000Z","published":"2025","updated":"2025-12-12T12:21:20.000Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}},"provider":{"data":{"id":"cern","type":"providers"}},"media":{"data":{"id":"10.5281/zenodo.17910992","type":"media"}},"references":{"data":[]},"citations":{"data":[]},"parts":{"data":[]},"partOf":{"data":[]},"versions":{"data":[]},"versionOf":{"data":[{"id":"10.5281/zenodo.17899072","type":"dois"}]}}}}