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Article History

Received: 9 June 2025

Accepted: 8 September 2025

First Online: 2 October 2025

Declarations

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: -Competing interests: The authors declare that they have no competing interests as defined by Springer. The research received funding from multiple sources, all of which are disclosed in the Funding section. These sources did not influence the interpretation or reporting of the results -Funding: S.F. and M.B. would like to acknowledge funding from Intel Corporation. C.G.A is thankful for support from the QuantERA grant EQUIP with the grant number PCI2022-133004, funded by Agencia Estatal de Investigación, Ministerio de Ciencia e Innovación, Gobierno de España, MCIN/AEI/10.13039/501100011033, and by the European Union NextGenerationEU/PRTR. Also from the Ministry for Digital Transformation and of Civil Service of the Spanish Government through the QUANTUM ENIA project call – Quantum Spain project, and by the European Union through the Recovery, Transformation and Resilience Plan – NextGenerationEU within the framework of the Digital Spain 2026 Agenda. H.S., C.N., W.M. work was supported by the German Federal Ministry of Education and Research (BMBF), funding program ‘quantum technologies—from basic research to market’, grant numbers 13N16092 and 13N16093. This work used the Dutch national e-infrastructure with the support of the SURF Cooperative using grant no. ElNF-5822. W.M. acknowledges support by the High-Tech Agenda of the Free State of Bavaria. This is all the funding we have received and everything there is to declare. Employment: The authors declare that there are no relevant past, present, or anticipated employment affiliations that may gain or lose financially from the publication of this manuscript. Financial Interests: The authors declare they have no financial interests. Non-Financial Interests: The authors declare they have no non-financial interests. - Availability of data and materials: not applicable - Authors’ contributions: not applicable.