{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T07:32:03Z","timestamp":1767598323626,"version":"3.41.0"},"reference-count":61,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T00:00:00Z","timestamp":1695859200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Quantum Comput."],"published-print":{"date-parts":[[2023,12,31]]},"abstract":"<jats:p>While quantum computing holds great potential in combinatorial optimization, electronic structure calculation, and number theory, the current era of quantum computing is limited by noisy hardware. Many quantum compilation approaches can mitigate the effects of imperfect hardware by optimizing quantum circuits for objectives such as critical path length. Few approaches consider quantum circuits in terms of the set of vendor-calibrated operations (i.e., native gates) available on target hardware. This manuscript expands the analytical and numerical approaches for optimizing quantum circuits at this abstraction level. We present a procedure for combining the strengths of analytical native gate-level optimization with numerical optimization. Although we focus on optimizing Toffoli gates on the IBMQ native gate set, the methods presented are generalizable to any gate and superconducting qubit architecture. Our optimized Toffoli gate implementation demonstrates an 18% reduction in infidelity compared with the canonical implementation as benchmarked on IBM Jakarta with quantum process tomography. Assuming the inclusion of multi-qubit cross-resonance (MCR) gates in the IBMQ native gate set, we produce Toffoli implementations with only six multi-qubit gates, a 25% reduction from the canonical eight multi-qubit implementations for linearly connected qubits.<\/jats:p>","DOI":"10.1145\/3609229","type":"journal-article","created":{"date-parts":[[2023,7,20]],"date-time":"2023-07-20T12:04:15Z","timestamp":1689854655000},"page":"1-19","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":8,"title":["Hardware-Conscious Optimization of the Quantum Toffoli Gate"],"prefix":"10.1145","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1288-7687","authenticated-orcid":false,"given":"Max Aksel","family":"Bowman","sequence":"first","affiliation":[{"name":"Rice University, Houston, TX"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1946-4537","authenticated-orcid":false,"given":"Pranav","family":"Gokhale","sequence":"additional","affiliation":[{"name":"Infleqtion, a division of ColdQuanta, Chicago, IL"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9924-2082","authenticated-orcid":false,"given":"Jeffrey","family":"Larson","sequence":"additional","affiliation":[{"name":"Argonne National Laboratory, Lemont, IL"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5509-5065","authenticated-orcid":false,"given":"Ji","family":"Liu","sequence":"additional","affiliation":[{"name":"Argonne National Laboratory, Lemont, IL"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8808-1367","authenticated-orcid":false,"given":"Martin","family":"Suchara","sequence":"additional","affiliation":[{"name":"Amazon, Seattle, WA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2023,9,28]]},"reference":[{"key":"e_1_3_1_2_2","volume-title":"Ceres Solver","author":"Agarwal Sameer","year":"2022","unstructured":"Sameer Agarwal, Keir Mierle, and The Ceres Solver Team. 2022. Ceres Solver. https:\/\/github.com\/ceres-solver\/ceres-solver"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.5281\/zenodo.2573505"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-019-1666-5"},{"key":"e_1_3_1_5_2","unstructured":"Jonathan M. Baker Casey Duckering Pranav Gokhale and Andrew Litteken. 2020. Quantum circuit benchmarks. https:\/\/github.com\/jmbaker94\/quantumcircuitbenchmarks"},{"key":"e_1_3_1_6_2","unstructured":"Jonathan M. Baker Casey Duckering Alexander Hoover and Frederic T. Chong. 2019. Decomposing quantum generalized Toffoli with an arbitrary number of ancilla. arxiv:1904.01671 [quant-ph]."},{"key":"e_1_3_1_7_2","doi-asserted-by":"publisher","DOI":"10.1103\/physreva.52.3457"},{"key":"e_1_3_1_8_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature13171"},{"key":"e_1_3_1_9_2","doi-asserted-by":"publisher","DOI":"10.1109\/ISCA45697.2020.00052"},{"key":"e_1_3_1_10_2","doi-asserted-by":"publisher","DOI":"10.5281\/ZENODO.5182845"},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.4230\/LIPIcs.TQC.2019.5"},{"key":"e_1_3_1_12_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.117.130503"},{"key":"e_1_3_1_13_2","unstructured":"Steven A. Cuccaro Thomas G. Draper Samuel A. Kutin and David Petrie Moulton. 2004. A new quantum ripple-carry addition circuit. arxiv:quant-ph\/0410184 [quant-ph]."},{"key":"e_1_3_1_14_2","doi-asserted-by":"publisher","DOI":"10.1145\/3466752.3480059"},{"key":"e_1_3_1_15_2","doi-asserted-by":"publisher","DOI":"10.1145\/3445814.3446718"},{"key":"e_1_3_1_16_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-017- 01904-7"},{"key":"e_1_3_1_17_2","unstructured":"Will Finigan Michael Cubeddu Thomas Lively Johannes Flick and Prineha Narang. 2018. Qubit allocation for noisy intermediate-scale quantum computers. arxiv:1810.08291 [quant-ph]."},{"key":"e_1_3_1_18_2","unstructured":"Craig Gidney. 2015. Constructing large controlled nots. https:\/\/algassert.com\/circuits\/2015\/06\/05\/Constructing-Large-Controlled-Nots.html"},{"key":"e_1_3_1_19_2","doi-asserted-by":"publisher","DOI":"10.1145\/3352460.3358313"},{"key":"e_1_3_1_20_2","doi-asserted-by":"publisher","DOI":"10.1109\/MICRO50266.2020.00027"},{"key":"e_1_3_1_21_2","doi-asserted-by":"publisher","DOI":"10.1109\/QCE52317.2021.00045"},{"key":"e_1_3_1_22_2","unstructured":"Pranav Gokhale Teague Tomesh Martin Suchara and Frederic T. Chong. 2021. Faster and more reliable quantum SWAPs via native gates. arxiv:2109.13199 [quant-ph]."},{"key":"e_1_3_1_23_2","doi-asserted-by":"publisher","DOI":"10.1145\/237814.237866"},{"key":"e_1_3_1_24_2","doi-asserted-by":"publisher","DOI":"10.3390\/a12020034"},{"key":"e_1_3_1_25_2","doi-asserted-by":"publisher","DOI":"10.1109\/mc.2008.209"},{"key":"e_1_3_1_26_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-019-1197-0"},{"key":"e_1_3_1_27_2","doi-asserted-by":"publisher","DOI":"10.1088\/2058-9565\/abe519"},{"key":"e_1_3_1_28_2","doi-asserted-by":"publisher","DOI":"10.1109\/tcad.2021.3057583"},{"key":"e_1_3_1_29_2","doi-asserted-by":"publisher","DOI":"10.1103\/physreva.95.042318"},{"key":"e_1_3_1_30_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.123.170503"},{"key":"e_1_3_1_31_2","doi-asserted-by":"publisher","DOI":"10.1145\/3297858.3304023"},{"key":"e_1_3_1_32_2","doi-asserted-by":"publisher","DOI":"10.48550\/arxiv.2302.02003"},{"key":"e_1_3_1_33_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.96.022330"},{"key":"e_1_3_1_34_2","doi-asserted-by":"publisher","DOI":"10.1007\/bfb0067700"},{"key":"e_1_3_1_35_2","doi-asserted-by":"publisher","DOI":"10.1145\/3373376.3378477"},{"key":"e_1_3_1_36_2","unstructured":"Paul Nation Hanhee Paik Andrew Cross and Zaira Nazario. 2021. The IBM Quantum heavy hex lattice. https:\/\/www.research.ibm.com\/blog\/heavy-hex-lattice"},{"key":"e_1_3_1_37_2","doi-asserted-by":"publisher","DOI":"10.1017\/cbo9780511976667"},{"key":"e_1_3_1_38_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-021-04182-y"},{"key":"e_1_3_1_39_2","first-page":"705","volume-title":"USENIX Annual Technical Conference","author":"Patel Tirthak","year":"2020","unstructured":"Tirthak Patel, Baolin Li, Rohan Basu Roy, and Devesh Tiwari. 2020. UREQA: Leveraging operation-aware error rates for effective quantum circuit mapping on NISQ-era quantum computers. In USENIX Annual Technical Conference. 705\u2013711. https:\/\/www.usenix.org\/conference\/atc20\/presentation\/patel"},{"key":"e_1_3_1_40_2","unstructured":"John Preskill. 2021. Quantum computing 40 years later. arxiv:2106.10522 [quant-ph]."},{"key":"e_1_3_1_41_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature10786"},{"key":"e_1_3_1_42_2","doi-asserted-by":"publisher","DOI":"10.1109\/TQE.2022.3170008"},{"key":"e_1_3_1_43_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.93.060302"},{"key":"e_1_3_1_44_2","doi-asserted-by":"publisher","DOI":"10.26421\/qic8.5-6-8"},{"key":"e_1_3_1_45_2","doi-asserted-by":"publisher","DOI":"10.1137\/s0097539795293172"},{"key":"e_1_3_1_46_2","doi-asserted-by":"publisher","DOI":"10.1145\/3548693"},{"key":"e_1_3_1_47_2","doi-asserted-by":"publisher","DOI":"10.1103\/PRXQuantum.1.020318"},{"key":"e_1_3_1_48_2","unstructured":"Frederic T. Chong Paige Frederick Palash Goiporia Pranav Gokhale Benjamin Hall Salahedeen Issa Stephanie Lee Andrew Litteken Victory Omole David Owusu-Antwi Michael Perlin Rich Rines Kaitlin N. Smith Noah Goss Akel Hashim Ravi Naik Ed Younis Daniel Lobser Christopher G Yale Benchen Huang and Ji Liu. 2023. Superstaq: Deep optimization of quantum programs. IEEE International Conference on Quantum Computing and Engineering (QCE) IEEE."},{"key":"e_1_3_1_49_2","doi-asserted-by":"publisher","DOI":"10.26421\/qic10.9-10-12"},{"key":"e_1_3_1_50_2","doi-asserted-by":"publisher","DOI":"10.1109\/iccad51958.2021.9643554"},{"key":"e_1_3_1_51_2","doi-asserted-by":"publisher","DOI":"10.1145\/3352460.3358257"},{"key":"e_1_3_1_52_2","doi-asserted-by":"publisher","DOI":"10.1145\/3352460.3358265"},{"key":"e_1_3_1_53_2","doi-asserted-by":"publisher","DOI":"10.1145\/3297858.3304007"},{"key":"e_1_3_1_54_2","unstructured":"PyQuOpt Development Team. 2022. PyQuOpt Research Software. https:\/\/github.com\/maxaksel\/Toffoli-Optimization"},{"key":"e_1_3_1_55_2","unstructured":"QuOpt Development Team. 2021. QuOpt Research Software. https:\/\/github.com\/maxaksel\/QuOpt"},{"key":"e_1_3_1_56_2","doi-asserted-by":"publisher","DOI":"10.21236\/ada082021"},{"key":"e_1_3_1_57_2","unstructured":"Teague Tomesh Nicholas Allen and Zain Saleem. 2022. Quantum-classical tradeoffs and multi-controlled quantum gate decompositions in variational algorithms. arxiv:2210.04378 [quant-ph]."},{"key":"e_1_3_1_58_2","doi-asserted-by":"publisher","DOI":"10.1088\/2058-9565\/aaa331"},{"key":"e_1_3_1_59_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41592-019-0686-2"},{"key":"e_1_3_1_60_2","doi-asserted-by":"publisher","DOI":"10.1103\/physrevlett.105.230503"},{"key":"e_1_3_1_61_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-019-13534-2"},{"key":"e_1_3_1_62_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevApplied.17.034074"}],"container-title":["ACM Transactions on Quantum Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3609229","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3609229","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T17:48:58Z","timestamp":1750182538000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3609229"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,28]]},"references-count":61,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,12,31]]}},"alternative-id":["10.1145\/3609229"],"URL":"https:\/\/doi.org\/10.1145\/3609229","relation":{},"ISSN":["2643-6809","2643-6817"],"issn-type":[{"type":"print","value":"2643-6809"},{"type":"electronic","value":"2643-6817"}],"subject":[],"published":{"date-parts":[[2023,9,28]]},"assertion":[{"value":"2022-09-16","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-06-21","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-09-28","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}