{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T19:50:06Z","timestamp":1780084206078,"version":"3.54.0"},"reference-count":25,"publisher":"Association for Computing Machinery (ACM)","issue":"3","funder":[{"name":"QEP grant","award":["NRF2021-QEP2-02-P05"],"award-info":[{"award-number":["NRF2021-QEP2-02-P05"]}]},{"name":"MoE AcRF Tier","award":["RT10\/23"],"award-info":[{"award-number":["RT10\/23"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Quantum Comput."],"published-print":{"date-parts":[[2025,9,30]]},"abstract":"<jats:p>\n            Efficient quantum arithmetic circuits are commonly found in numerous quantum algorithms of practical significance. To date, the logarithmic-depth quantum adders include a constant coefficient\n            <jats:italic toggle=\"yes\">k<\/jats:italic>\n            \u2265 2 while achieving the Toffoli-Depth of\n            <jats:italic toggle=\"yes\">k<\/jats:italic>\n            log\n            <jats:italic toggle=\"yes\">n<\/jats:italic>\n            + \ud835\udcaa(1). In this work, 160 alternative compositions of the carry-propagation structure are comprehensively explored to determine the optimal depth structure for a quantum adder. By extensively studying these structures, it is shown that an exact Toffoli-Depth of log\n            <jats:italic toggle=\"yes\">n<\/jats:italic>\n            + \ud835\udcaa(1) is achievable. This presents a reduction of Toffoli-Depth by almost 50% compared to the best known quantum adder circuits presented to date. We demonstrate a further possible design by incorporating a different expansion of propagate and generate forms, as well as an extension of the modular framework. Our article elaborates on these designs, supported by detailed theoretical analyses and simulation-based studies, firmly substantiating our claims of optimality within all possible configurations outlined in this work. The results also mirror similar improvements, recently reported in classical adder circuit complexity.\n          <\/jats:p>","DOI":"10.1145\/3743691","type":"journal-article","created":{"date-parts":[[2025,6,10]],"date-time":"2025-06-10T07:35:31Z","timestamp":1749540931000},"page":"1-16","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":5,"title":["Optimal Toffoli-Depth Quantum Adder"],"prefix":"10.1145","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-9128-1857","authenticated-orcid":false,"given":"Siyi","family":"Wang","sequence":"first","affiliation":[{"name":"College of Computing and Data Science, Nanyang Technological University","place":["Singapore, Singapore"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-0956-0123","authenticated-orcid":false,"given":"Ankit","family":"Mondal","sequence":"additional","affiliation":[{"name":"Indian Institute of Technology Delhi","place":["New Delhi, India"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8818-6983","authenticated-orcid":false,"given":"Anupam","family":"Chattopadhyay","sequence":"additional","affiliation":[{"name":"College of Computing and Data Science, Nanyang Technological University","place":["Singapore, Singapore"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2025,7,12]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/TC.1982.1675982"},{"key":"e_1_3_2_3_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\/quant-ph\/0410184. Retrieved from https:\/\/arxiv.org\/abs\/quant-ph\/0410184"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.26421\/QIC6.4-5-4"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.111.052611"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.22331\/q-2018-06-18-74"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1145\/3147215"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1109\/TC.1973.5009159"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","unstructured":"Sejin Lim Hyunjun Kim Kyungbae Jang Siyi Wang Anubhab Baksi Anupam Chattopadhyay and Hwajeong Seo. 2023. Optimized quantum circuit implementation of payoff function. In 2023 IFIP\/IEEE 31st International Conference on Very Large Scale Integration (VLSI-SoC). 1\u20136. 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Efficient depth optimization in quantum addition and modular arithmetic with Ling structure. In Proceedings of the IFIP\/IEEE International Conference on Very Large Scale Integration-System on a Chip. Springer, 73\u201389."},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1109\/VLSI-SoC57769.2023.10321948"},{"issue":"2288","key":"e_1_3_2_23_2","first-page":"20230392","article-title":"A comprehensive study of quantum arithmetic circuits","volume":"383","author":"Wang Siyi","year":"2025","unstructured":"Siyi Wang, Xiufan Li, Wei Jie Bryan Lee, Suman Deb, Eugene Lim, and Anupam Chattopadhyay. 2025. A comprehensive study of quantum arithmetic circuits. Philosophical Transactions A 383, 2288 (2025), 20230392.","journal-title":"Philosophical Transactions A"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","unstructured":"Siyi Wang Eugene Lim and Anupam Chattopadhyay. 2024. Boosting the efficiency of quantum divider through effective design space exploration. 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