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We show that a large family of distributions can be encoded as low-entanglement states of the quantum register. These states can be efficiently created in a quantum computer, but they are also efficiently stored, manipulated and probed using Matrix-Product States techniques. Inspired by this idea, we present eight quantum-inspired numerical analysis algorithms, that include Fourier sampling, interpolation, differentiation and integration of partial derivative equations. These algorithms combine classical ideas \u2013 finite-differences, spectral methods \u2013 with the efficient encoding of quantum registers, and well known algorithms, such as the Quantum Fourier Transform. <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mtext class=\"MJX-tex-mathit\" mathvariant=\"italic\">When these heuristic methods work<\/mml:mtext><\/mml:mrow><\/mml:math>, they provide an exponential speed-up over other classical algorithms, such as Monte Carlo integration, finite-difference and fast Fourier transforms (FFT). But even when they don't, some of these algorithms can be translated back to a quantum computer to implement a similar task.<\/jats:p>","DOI":"10.22331\/q-2021-04-15-431","type":"journal-article","created":{"date-parts":[[2021,4,15]],"date-time":"2021-04-15T16:48:10Z","timestamp":1618505290000},"page":"431","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":50,"title":["Quantum-inspired algorithms for multivariate analysis: from interpolation to partial differential equations"],"prefix":"10.22331","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8993-4624","authenticated-orcid":false,"given":"Juan Jos\u00e9","family":"Garc\u00eda-Ripoll","sequence":"first","affiliation":[{"name":"Institute of Fundamental Physics, Calle Serrano 113b, 28006 Madrid, Spain"}]}],"member":"9598","published-online":{"date-parts":[[2021,4,15]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"C. Zalka. 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