{"data":{"id":"10.5281/zenodo.17889778","type":"dois","attributes":{"doi":"10.5281/zenodo.17889778","prefix":"10.5281","suffix":"zenodo.17889778","identifiers":[{"identifier":"oai:zenodo.org:17889778","identifierType":"oai"},{"identifier":"https://github.com/QDaria/tqrc","identifierType":"URL"}],"alternateIdentifiers":[{"alternateIdentifierType":"oai","alternateIdentifier":"oai:zenodo.org:17889778"},{"alternateIdentifierType":"URL","alternateIdentifier":"https://github.com/QDaria/tqrc"}],"creators":[{"name":"Houshmand, Daniel Mo","nameType":"Personal","givenName":"Daniel Mo","familyName":"Houshmand","affiliation":["QDaria"],"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":"Fundamental Limitations of Topological Quantum Reservoir Computing: A No-Go Theorem for Fibonacci Anyonic Systems"}],"publisher":"Zenodo","container":{},"publicationYear":2025,"subjects":[{"subject":"topological quantum computing"},{"subject":"quantum reservoir computing"},{"subject":"Fibonacci anyons"},{"subject":"no-go theorem"},{"subject":"quantum machine learning"},{"subject":"reservoir computing"},{"subject":"Quantum computers","subjectScheme":"EuroSciVoc"}],"contributors":[],"dates":[{"date":"2025-12-11","dateType":"Issued"},{"date":"2025-12-11","dateType":"Issued","dateInformation":"Preprint release   "}],"language":"en","types":{"ris":"GEN","bibtex":"misc","citeproc":"article","schemaOrg":"CreativeWork","resourceType":"","resourceTypeGeneral":"Preprint"},"relatedIdentifiers":[{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.17889777","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"},{"rights":"Copyright (C) 2025 Daniel Mo Houshmand","rightsUri":"http://rightsstatements.org/vocab/InC/1.0/"}],"descriptions":[{"description":"Abstract—Reservoir computing exploits high-dimensional nonlinear dynamics to solve temporal prediction tasks with minimal training\n\ncost. We investigate Topological Quantum Reservoir Computing (TQRC), which proposes to harness the braiding dynamics of\n\nFibonacci anyons as quantum reservoirs. Our comprehensive analysis reveals a fundamental tension: the very properties that make\n\ntopological systems attractive for quantum computation (unitary evolution and information preservation) fundamentally oppose the\n\nEcho State Property (ESP) required for reservoir computing.\n\nWe demonstrate rigorously that pure unitary TQRC violates the ESP: unitary evolution preserves distances in Hilbert space,\n\npreventing the fading memory necessary for reservoir computing. On Mackey-Glass time series benchmarks, pure unitary TQRC\n\nachieves NRMSE ≈1.0 (equivalent to random guessing). Introducing controlled dissipation recovers functional reservoir dynamics\n\n(best NRMSE = 0.44), but at the cost of sacrificing topological protection.\n\nCritically, we show that classical Echo State Networks outperform dissipative TQRC by 20× at equivalent state-space dimension\n\n(ESN NRMSE = 0.02 vs. TQRC NRMSE = 0.44 for d= 13). We identify four root causes: (1) probability readout constrains states to\n\nthe simplex, (2) measurement destroys phase information, (3) |·|2 provides weaker nonlinearity than tanh, and (4) structured braid\n\nmatrices limit state-space utilization.\n\nThese results constitute a no-go theorem for topological quantum reservoir computing: topological protection and reservoir computing\n\nfunctionality represent fundamentally competing requirements. This finding provides essential guidance for the quantum machine\n\nlearning community, establishing that topological protection should not be pursued as a route to quantum reservoir computing\n\nadvantage.\n\nIndex Terms—Topological quantum computing, Fibonacci anyons, reservoir computing, echo state property, quantum machine\n\nlearning, negative results","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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