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The LEAP algorithm improves scaling across these dimensions using iterative circuit synthesis, incremental reoptimization, dimensionality reduction, and improved numerical optimization. LEAP draws on the design of the optimal synthesis algorithm QSearch by extending it with an incremental approach to determine constant prefix solutions for a circuit. By narrowing the search space, LEAP improves scalability from four to six qubit circuits. LEAP was evaluated with known quantum circuits such as QFT and physical simulation circuits like the VQE, TFIM, and QITE. LEAP can compile four qubit unitaries up to 59\u00d7 faster than QSearch and five and six qubit unitaries with up to 1.2\u00d7 fewer CNOTs compared to the QFAST package. LEAP can reduce the CNOT count by up to 36\u00d7, or 7\u00d7 on average, compared to the CQC Tket compiler. Despite its heuristics, LEAP has generated optimal circuits for many test cases with\n            <jats:italic>a priori<\/jats:italic>\n            known solutions. The techniques introduced by LEAP are applicable to other numerical optimization based synthesis approaches.\n          <\/jats:p>","DOI":"10.1145\/3548693","type":"journal-article","created":{"date-parts":[[2022,8,9]],"date-time":"2022-08-09T11:39:40Z","timestamp":1660045180000},"page":"1-23","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":33,"title":["LEAP: Scaling Numerical Optimization Based Synthesis Using an Incremental Approach"],"prefix":"10.1145","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9440-9576","authenticated-orcid":false,"given":"Ethan","family":"Smith","sequence":"first","affiliation":[{"name":"University of California, Berkeley"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6543-5131","authenticated-orcid":false,"given":"Marc Grau","family":"Davis","sequence":"additional","affiliation":[{"name":"University of California, Berkeley"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9924-2082","authenticated-orcid":false,"given":"Jeffrey","family":"Larson","sequence":"additional","affiliation":[{"name":"Argonne National Laboratory, Lemont IL"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1306-1860","authenticated-orcid":false,"given":"Ed","family":"Younis","sequence":"additional","affiliation":[{"name":"Lawrence Berkeley National Laboratory"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3542-1553","authenticated-orcid":false,"given":"Lindsay Bassman","family":"Oftelie","sequence":"additional","affiliation":[{"name":"Lawrence Berkeley National Laboratory"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3490-904X","authenticated-orcid":false,"given":"Wim","family":"Lavrijsen","sequence":"additional","affiliation":[{"name":"Lawrence Berkeley National Laboratory"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7845-2427","authenticated-orcid":false,"given":"Costin","family":"Iancu","sequence":"additional","affiliation":[{"name":"Lawrence Berkeley National Laboratory"}]}],"member":"320","published-online":{"date-parts":[[2023,2,10]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.93.032318"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2005.855930"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/18\/6\/063029"},{"key":"e_1_3_2_5_2","first-page":"arXiv:1807.0080","article-title":"Quantum-assisted quantum compiling","author":"Khatri Sumeet","year":"2018","unstructured":"Sumeet Khatri, Ryan LaRose, Alexander Poremba, Lukasz Cincio, Andrew T. 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