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The algorithm is deterministic, does not require ancillary qubits, and does not require QR decompositions. The circuit prepares such an L<\/mml:mi><\/mml:math>-qubit state with M<\/mml:mi><\/mml:math> down-spins using (<\/mml:mo><\/mml:mrow>L<\/mml:mi>M<\/mml:mi><\/mml:mfrac>)<\/mml:mo><\/mml:mrow><\/mml:mrow>&#x2212;<\/mml:mo>1<\/mml:mn><\/mml:math> multi-controlled rotation gates and 2<\/mml:mn>M<\/mml:mi>(<\/mml:mo>L<\/mml:mi>&#x2212;<\/mml:mo>M<\/mml:mi>)<\/mml:mo><\/mml:math> CNOT-gates.<\/jats:p>","DOI":"10.22331\/q-2024-10-24-1510","type":"journal-article","created":{"date-parts":[[2024,10,24]],"date-time":"2024-10-24T11:36:53Z","timestamp":1729769813000},"page":"1510","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":11,"title":["Deterministic Bethe state preparation"],"prefix":"10.22331","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6818-8159","authenticated-orcid":false,"given":"David","family":"Raveh","sequence":"first","affiliation":[{"name":"Department of Physics, PO Box 248046, University of Miami, Coral Gables, FL 33124 USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1000-3400","authenticated-orcid":false,"given":"Rafael I.","family":"Nepomechie","sequence":"additional","affiliation":[{"name":"Department of Physics, PO Box 248046, University of Miami, Coral Gables, FL 33124 USA"}]}],"member":"9598","published-online":{"date-parts":[[2024,10,24]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"John Preskill. ``Quantum computing 40 years later''. 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