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Using this, we analyze which small sets of XX-type interactions cause the greatest improvement in expected infidelity under experimentally-motivated error models. For the exact circuit synthesis of Haar-randomly selected two-qubit operations, we find an improvement in estimated infidelity by 31.4% when including alongside CX its square- and cube-roots, near to the optimal limit of 36.9% obtained by including all fractional applications of CX.<\/jats:p>","DOI":"10.22331\/q-2022-04-27-696","type":"journal-article","created":{"date-parts":[[2022,4,27]],"date-time":"2022-04-27T13:09:28Z","timestamp":1651064968000},"page":"696","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":14,"title":["Optimal synthesis into fixed XX interactions"],"prefix":"10.22331","volume":"6","author":[{"given":"Eric C.","family":"Peterson","sequence":"first","affiliation":[{"name":"IBM Quantum, San Jose, CA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lev S.","family":"Bishop","sequence":"additional","affiliation":[{"name":"IBM Quantum, Yorktown Heights, NY, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ali","family":"Javadi-Abhari","sequence":"additional","affiliation":[{"name":"IBM Quantum, Yorktown Heights, NY, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2022,4,27]]},"reference":[{"key":"0","unstructured":"Charles H. 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