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Here, we show that one can achieve similar scaling even for arbitrary basis sets (which can be hundreds of times more compact than plane waves) by using qubitized quantum walks in a fashion that takes advantage of structure in the Coulomb operator, either by directly exploiting sparseness, or via a low rank tensor factorization. We provide circuits for several variants of our algorithm (which all improve over the scaling of prior methods) including one with <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mover><mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">O<\/mml:mi><mml:mo>~<\/mml:mo><\/mml:mover><\/mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:msup><mml:mi>N<\/mml:mi><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mn>3<\/mml:mn><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo>\/<\/mml:mo><\/mml:mrow><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:msup><mml:mi>\u03bb<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math> T complexity, where <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>N<\/mml:mi><\/mml:math> is number of orbitals and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03bb<\/mml:mi><\/mml:math> is the 1-norm of the chemistry Hamiltonian. We deploy our algorithms to simulate the FeMoco molecule (relevant to Nitrogen fixation) and obtain circuits requiring about seven hundred times less surface code spacetime volume than prior quantum algorithms for this system, despite us using a larger and more accurate active space.<\/jats:p>","DOI":"10.22331\/q-2019-12-02-208","type":"journal-article","created":{"date-parts":[[2019,12,2]],"date-time":"2019-12-02T11:47:15Z","timestamp":1575287235000},"page":"208","source":"Crossref","is-referenced-by-count":158,"title":["Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization"],"prefix":"10.22331","volume":"3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3446-1449","authenticated-orcid":false,"given":"Dominic W.","family":"Berry","sequence":"first","affiliation":[{"name":"Department of Physics and Astronomy, Macquarie University, Sydney, NSW 2109, Australia"}]},{"given":"Craig","family":"Gidney","sequence":"additional","affiliation":[{"name":"Google Research, Venice, CA 90291, United States"}]},{"given":"Mario","family":"Motta","sequence":"additional","affiliation":[{"name":"Division of Chemistry, California Institute of Technology, Pasadena, CA 91125, United States"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2809-0509","authenticated-orcid":false,"given":"Jarrod R.","family":"McClean","sequence":"additional","affiliation":[{"name":"Google Research, Venice, CA 90291, United States"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6979-9533","authenticated-orcid":false,"given":"Ryan","family":"Babbush","sequence":"additional","affiliation":[{"name":"Google Research, Venice, CA 90291, United States"}]}],"member":"9598","published-online":{"date-parts":[[2019,12,2]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"R. 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