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In this work, we show that controlled single-excitation gates in the form of Givens rotations are universal for particle-conserving unitaries. Single-excitation gates describe an arbitrary U<\/mml:mi>(<\/mml:mo>2<\/mml:mn>)<\/mml:mo><\/mml:math> rotation on the two-qubit subspace spanned by the states |<\/mml:mo><\/mml:mrow>01<\/mml:mn>&#x27E9;<\/mml:mo>,<\/mml:mo>|<\/mml:mo><\/mml:mrow>10<\/mml:mn>&#x27E9;<\/mml:mo><\/mml:math>, while leaving other states unchanged \u2013 a transformation that is analogous to a single-qubit rotation on a dual-rail qubit. The proof is constructive, so our result also provides an explicit method for compiling arbitrary particle-conserving unitaries. Additionally, we describe a method for using controlled single-excitation gates to prepare an arbitrary state of a fixed number of particles. We derive analytical gradient formulas for Givens rotations as well as decompositions into single-qubit and CNOT gates. Our results offer a unifying framework for quantum computational chemistry where every algorithm is a unique recipe built from the same universal ingredients: Givens rotations.<\/jats:p>","DOI":"10.22331\/q-2022-06-20-742","type":"journal-article","created":{"date-parts":[[2022,6,20]],"date-time":"2022-06-20T15:37:59Z","timestamp":1655739479000},"page":"742","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":63,"title":["Universal quantum circuits for quantum chemistry"],"prefix":"10.22331","volume":"6","author":[{"given":"Juan Miguel","family":"Arrazola","sequence":"first","affiliation":[{"name":"Xanadu, Toronto, ON, M5G 2C8, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Olivia","family":"Di Matteo","sequence":"additional","affiliation":[{"name":"Xanadu, Toronto, ON, M5G 2C8, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nicol\u00e1s","family":"Quesada","sequence":"additional","affiliation":[{"name":"Xanadu, Toronto, ON, M5G 2C8, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Soran","family":"Jahangiri","sequence":"additional","affiliation":[{"name":"Xanadu, Toronto, ON, M5G 2C8, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alain","family":"Delgado","sequence":"additional","affiliation":[{"name":"Xanadu, Toronto, ON, M5G 2C8, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nathan","family":"Killoran","sequence":"additional","affiliation":[{"name":"Xanadu, Toronto, ON, M5G 2C8, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2022,6,20]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Sam McArdle, Suguru Endo, Alan Aspuru-Guzik, Simon C Benjamin, and Xiao Yuan. ``Quantum computational chemistry''. 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