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By combining projective measurements with conditional feedback, the protocol learns state preparation strategies that extend beyond unitary-only methods, leveraging measurement-based shortcuts to reduce circuit depth. Using the spin-1 Affleck-Kennedy-Lieb-Tasaki state as a benchmark, the protocol learns high-fidelity state preparation by overcoming a family of measurement induced local minima through adjustments of parameter update frequencies and ancilla regularization. Despite these efforts, optimization remains challenging due to the highly non-convex landscapes inherent to variational circuits. The approach is extended to larger systems using translationally invariant ans\u00c3\u00a4tze and recurrent neural networks for feedback, demonstrating scalability. Additionally, the successful preparation of a specific AKLT state with desired edge modes highlights the potential to discover new state preparation protocols where none currently exist. These results indicate that integrating measurement and feedback into variational quantum algorithms provides a promising framework for quantum state preparation.<\/jats:p>","DOI":"10.22331\/q-2025-07-11-1792","type":"journal-article","created":{"date-parts":[[2025,7,11]],"date-time":"2025-07-11T16:17:51Z","timestamp":1752250671000},"page":"1792","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Learning Feedback Mechanisms for Measurement-Based Variational Quantum State Preparation"],"prefix":"10.22331","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3519-5931","authenticated-orcid":false,"given":"Daniel","family":"Alcalde Puente","sequence":"first","affiliation":[{"name":"Forschungszentrum J\u00fclich, Institute of Quantum Control, Peter Gr\u00fcnberg Institut (PGI-8), 52425 J\u00fclich, Germany"},{"name":"Institute for Theoretical Physics, University of Cologne, 50937 K\u00f6ln, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8283-1005","authenticated-orcid":false,"given":"Matteo","family":"Rizzi","sequence":"additional","affiliation":[{"name":"Forschungszentrum J\u00fclich, Institute of Quantum Control, Peter Gr\u00fcnberg Institut (PGI-8), 52425 J\u00fclich, Germany"},{"name":"Institute for Theoretical Physics, University of Cologne, 50937 K\u00f6ln, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2025,7,11]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"John Preskill. ``Quantum Computing in the NISQ era and beyond''. 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