{"data":{"id":"10.5281/zenodo.18371699","type":"dois","attributes":{"doi":"10.5281/zenodo.18371699","prefix":"10.5281","suffix":"zenodo.18371699","identifiers":[{"identifier":"oai:zenodo.org:18371699","identifierType":"oai"},{"identifier":"https://github.com/QDaria/tqrc","identifierType":"URL"},{"identifier":"https://github.com/MoHoushmand/tqrc","identifierType":"URL"}],"alternateIdentifiers":[{"alternateIdentifierType":"oai","alternateIdentifier":"oai:zenodo.org:18371699"},{"alternateIdentifierType":"URL","alternateIdentifier":"https://github.com/QDaria/tqrc"},{"alternateIdentifierType":"URL","alternateIdentifier":"https://github.com/MoHoushmand/tqrc"}],"creators":[{"name":"Houshmand, Daniel Mo","nameType":"Personal","givenName":"Daniel Mo","familyName":"Houshmand","affiliation":["QDaria"],"nameIdentifiers":[{"nameIdentifier":"0009-0008-2270-5454","nameIdentifierScheme":"ORCID"}]}],"titles":[{"title":"The Fundamental Tension in Topological Quantum Reservoir Computing: Why Unitarity Opposes the Echo State Property"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"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":"2026-01-26","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":"3.0.0","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 - Q | D∂rıα⟩","rightsUri":"http://rightsstatements.org/vocab/InC/1.0/"}],"descriptions":[{"description":"Reservoir computing exploits high-dimensional nonlinear dynamics to solve temporal prediction tasks with minimal training cost. We investigate Topological Quantum Reservoir Computing (TQRC), which proposes to harness the braiding dynamics of non-Abelian Fibonacci Anyons as Quantum Reservoirs. Our analysis reveals a fundamental tension: the very properties that make topological systems attractive for quantum computation (unitary evolution and information preservation) fundamentally oppose the Echo State Property (ESP) required for reservoir computing. We demonstrate rigorously that pure unitary TQRC violates the ESP: unitary evolution preserves distances in Hilbert space, preventing the fading memory necessary for reservoir computing. On Mackey-Glass time series benchmarks, pure unitary TQRC achieves NRMSE ≈ 1.0 (equivalent to random guessing). Introducing controlled dissipation with enhanced complex amplitude readout achieves best NRMSE = 0.44, but at the cost of sacrificing topological protection. Comparison against classical ESN baseline reveals a 20× performance gap at equivalent state-space dimension (ESN NRMSE = 0.02 vs. TQRC NRMSE = 0.44 for d = 13, Cohen’s d \u003e 200, p \u003c 10−65), quantifying the practical cost of Echo State Property (ESP) violation. We identify four structural causes: \n\n\n\nprobability readout constrains states to the simplex, \n\nmeasurement destroys phase information, \n\n| · |2 provides weaker nonlinearity than tanh, and \n\nstructured braid matrices limit state-space utilization.\n\n\nThese results constitute a no-go theorem for topological quantum reservoir computing on chaotic prediction tasks: topological protection and reservoir computing functionality represent fundamentally competing requirements. Notably, TQRC performs comparably to ESN on memory-focused tasks (NARMA-10), suggesting task-dependent applicability. This finding provides essential guidance for the quantum machine learning community, establishing that topological protection should not be pursued as a route to quantum reservoir computing advantage for chaotic time series prediction. \n\nIndex Terms—Topological quantum computing, Fibonacci anyons, reservoir computing, echo state property, quantum machine learning, negative results","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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