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We develop protocols for preparing quantum states whose amplitudes encode multivariate functions by linearly combining block-encodings of Fourier and Chebyshev basis functions. Without relying on arithmetic circuits, quantum Fourier transforms, or multivariate quantum signal processing, our algorithms are simpler and more effective than previous proposals. We analyze requirements both asymptotically and pragmatically in terms of near\/medium-term resources. Numerically, we prepare bivariate Student&apos;s t-distributions, 2D Ricker wavelets and electron wavefunctions in a 3D Coulomb potential, which are initial states with potential applications in finance, physics and chemistry simulations. Finally, we prepare bivariate Gaussian distributions on the Quantinuum H2-1 trapped-ion quantum processor using 24 qubits and up to 237 two-qubit gates.<\/jats:p>","DOI":"10.22331\/q-2025-04-09-1703","type":"journal-article","created":{"date-parts":[[2025,4,9]],"date-time":"2025-04-09T14:40:16Z","timestamp":1744209616000},"page":"1703","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":9,"title":["Quantum state preparation for multivariate functions"],"prefix":"10.22331","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1605-9141","authenticated-orcid":false,"given":"Matthias","family":"Rosenkranz","sequence":"first","affiliation":[{"name":"Quantinuum, Partnership House, Carlisle Place, London SW1P 1BX, United Kingdom"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7631-6528","authenticated-orcid":false,"given":"Eric","family":"Brunner","sequence":"additional","affiliation":[{"name":"Quantinuum, Partnership House, Carlisle Place, London SW1P 1BX, United Kingdom"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-7630-6081","authenticated-orcid":false,"given":"Gabriel","family":"Marin-Sanchez","sequence":"additional","affiliation":[{"name":"Quantinuum, Partnership House, Carlisle Place, London SW1P 1BX, United Kingdom"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5819-9129","authenticated-orcid":false,"given":"Nathan","family":"Fitzpatrick","sequence":"additional","affiliation":[{"name":"Quantinuum, Terrington House, 13-15 Hills Road, Cambridge CB2 1NL, United Kingdom"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2186-0379","authenticated-orcid":false,"given":"Silas","family":"Dilkes","sequence":"additional","affiliation":[{"name":"Quantinuum, Terrington House, 13-15 Hills Road, Cambridge CB2 1NL, United Kingdom"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-4023-8701","authenticated-orcid":false,"given":"Yao","family":"Tang","sequence":"additional","affiliation":[{"name":"Quantinuum, Terrington House, 13-15 Hills Road, Cambridge CB2 1NL, United Kingdom"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1802-5260","authenticated-orcid":false,"given":"Yuta","family":"Kikuchi","sequence":"additional","affiliation":[{"name":"Quantinuum K.K., Otemachi Financial City Grand Cube 3F, 1-9-2 Otemachi, Chiyoda-ku, Tokyo, Japan"},{"name":"Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), RIKEN, Wako, Saitama 351-0198, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0231-1729","authenticated-orcid":false,"given":"Marcello","family":"Benedetti","sequence":"additional","affiliation":[{"name":"Quantinuum, Partnership House, Carlisle Place, London SW1P 1BX, United Kingdom"}]}],"member":"9598","published-online":{"date-parts":[[2025,4,9]]},"reference":[{"key":"0","unstructured":"Sarah K. 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