{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T09:22:05Z","timestamp":1787822525452,"version":"build-2784847793"},"reference-count":35,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T00:00:00Z","timestamp":1787702400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62302318"],"award-info":[{"award-number":["62302318"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"award":["62302318"],"award-info":[{"award-number":["62302318"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Shenzhen Science and Technology Program","award":["20231124122522001"],"award-info":[{"award-number":["20231124122522001"]}]},{"name":"Research Projects of Department of Education of Guangdong Province","award":["2024KTSCX050"],"award-info":[{"award-number":["2024KTSCX050"]}]},{"award":["2024KTSCX050"],"award-info":[{"award-number":["2024KTSCX050"]}],"id":[{"id":"https:\/\/ror.org\/01s5gyw91","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Shenzhen Polytechnic University Research Fund","award":["6023310008K"],"award-info":[{"award-number":["6023310008K"]}]},{"name":"Shenzhen Polytechnic University Research Fund","award":["6026310054K"],"award-info":[{"award-number":["6026310054K"]}]},{"award":["6023310008K"],"award-info":[{"award-number":["6023310008K"]}],"id":[{"id":"https:\/\/ror.org\/00d2w9g53","id-type":"ROR","asserted-by":"publisher"}]},{"award":["6026310054K"],"award-info":[{"award-number":["6026310054K"]}],"id":[{"id":"https:\/\/ror.org\/00d2w9g53","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Institute for Economic and Social Development at Shenzhen Polytechnic University","award":["6025310002Q"],"award-info":[{"award-number":["6025310002Q"]}]},{"award":["6025310002Q"],"award-info":[{"award-number":["6025310002Q"]}],"id":[{"id":"https:\/\/ror.org\/00d2w9g53","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Quantum federated learning (QFL) enables collaborative training of variational quantum circuits across decentralized clients, but client drift under non-IID data distributions degrades standard Federated Averaging (FedAvg). Existing aggregation methods either introduce tunable hyperparameters that depend on unknown data heterogeneity or incur structural costs such as order-dependent error propagation. We propose Kernel-Weighted Aggregation (KWA), a hyperparameter-free aggregation strategy that constructs a non-parametric kernel density estimate over the received client parameter vectors at each communication round. Clients in high-density regions receive greater voting power, and isolated clients are automatically attenuated. The kernel bandwidth is the median of all pairwise squared distances. We evaluate KWA against six state-of-the-art QFL methods and five classical robust baselines on five binary MNIST digit-pair tasks under IID, Dir(0.5), and Dir(0.1) distributions with a unified four-qubit benchmark. Under IID data, KWA recovers the performance of FedAvg. Under Dir(0.5), KWA attains the highest average accuracy (0.7120), followed by FedAvg (0.7093). The margin at N=4 clients is not statistically significant. It grows to +0.023 at N=16 in the client scaling experiment. Under this distribution, the five classical robust baselines also rank below FedAvg. Under Dir(0.1), KWA exceeds FedAvg by 0.028 on average, with a pooled paired t-test p=0.068. Larger-circuit and three-class experiments show that the advantage does not yet transfer consistently beyond the four-qubit binary setting. KWA thus provides a hyperparameter-free aggregation strategy that recovers FedAvg under IID conditions, adapts to client drift, and requires no manually tuned hyperparameters.<\/jats:p>","DOI":"10.3390\/e28090958","type":"journal-article","created":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T12:59:57Z","timestamp":1787749197000},"page":"958","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Kernel-Weighted Aggregation for Hyperparameter-Free Quantum Federated Learning"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8439-4526","authenticated-orcid":false,"given":"Rui","family":"Huang","sequence":"first","affiliation":[{"name":"School of Artificial Intelligence, Shenzhen Polytechnic University, Shenzhen 518055, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1007\/BF01886518","article-title":"Quantum mechanical computers","volume":"16","author":"Feynman","year":"1986","journal-title":"Found. 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