{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T14:29:27Z","timestamp":1770820167941,"version":"3.50.1"},"reference-count":69,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2025,1,14]],"date-time":"2025-01-14T00:00:00Z","timestamp":1736812800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Transactions on Quantum Computing"],"published-print":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>Combinatorial Optimization (CO) problems exhibit exponential complexity, constraining classical computers from providing fast and satisfactory outcomes. Quantum Computers (QCs) can effectively find optimal or near-optimal solutions by exploring the solutions space of a problem encoded in a qubits system, exploiting principles of quantum mechanics. However, non-idealities and high costs limit their availability. These can be overcome by emulating QCs on cheaper and more accessible classical computing platforms, like Field-Programmable Gate Arrays (FPGAs).<\/jats:p>\n          <jats:p>This article presents a digital architecture, implementing the Ising-compatible Simulated Adiabatic Bifurcation algorithm. It mimics the quantum adiabatic evolution of a network of non-linear Kerr oscillators. The architecture, described in VHDL and targeting FPGAs, consists of processing elements for computing the Kerr oscillators\u2019 evolution, a set of units considering their Ising-related interactions and an evolution variables update unit. The proposed approach includes a speedup-targeting approximation of the algorithm, a method for handling single-variable constraints, and a software model that allows architecture customization for specific problems. Tests were conducted using an Altera Cyclone V SoC with FPGA logic and the Nios II processor for interface purposes. The results demonstrate the functionality of the architecture and its scalability with the problem size, making it suitable for real-world applications.<\/jats:p>","DOI":"10.1145\/3665281","type":"journal-article","created":{"date-parts":[[2024,5,29]],"date-time":"2024-05-29T11:47:43Z","timestamp":1716983263000},"page":"1-50","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Improving the exploitability of Simulated Adiabatic Bifurcation through a flexible and open-source digital architecture"],"prefix":"10.1145","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3364-1114","authenticated-orcid":false,"given":"Deborah","family":"Volpe","sequence":"first","affiliation":[{"name":"Department of Electronics and Telecommunications, Politecnico di Torino, Torino, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5563-8277","authenticated-orcid":false,"given":"Giovanni Amedeo","family":"Cirillo","sequence":"additional","affiliation":[{"name":"Department of Electronics and Telecommunications, Politecnico di Torino, Torino, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5249-9259","authenticated-orcid":false,"given":"Maurizio","family":"Zamboni","sequence":"additional","affiliation":[{"name":"Department of Electronics and Telecommunications, Politecnico di Torino, Torino, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8721-9990","authenticated-orcid":false,"given":"Mariagrazia","family":"Graziano","sequence":"additional","affiliation":[{"name":"Department of Applied Science and Technology, Politecnico di Torino, Torino, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8520-906X","authenticated-orcid":false,"given":"Giovanna","family":"Turvani","sequence":"additional","affiliation":[{"name":"Department of Electronics and Telecommunications, Politecnico di Torino, Torino, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2025,1,14]]},"reference":[{"key":"e_1_3_1_2_2","unstructured":"Intel. Intel Xeon Gold 6134 Processor - Product Specification. Retrieved October 25 2021 from https:\/\/ark.intel.com\/content\/www\/us\/en\/ark\/products\/120493\/intel-xeon-gold-6134-processor-24-75m-cache-3-20-ghz.html"},{"key":"e_1_3_1_3_2","volume-title":"Python Package Dimod","author":"D-Wave Systems Inc","unstructured":"D-Wave Systems Inc. Python Package Dimod. https:\/\/github.com\/dwavesystems\/dimod"},{"key":"e_1_3_1_4_2","doi-asserted-by":"crossref","unstructured":"Amira Abbas Andris Ambainis Brandon Augustino Andreas B\u00e4rtschi Harry Buhrman Carleton Coffrin Giorgio Cortiana Vedran Dunjko Daniel J. Egger Bruce G. Elmegreen Nicola Franco Filippo Fratini Bryce Fuller Julien Gacon Constantin Gonciulea Sander Gribling Swati Gupta Stuart Hadfield Raoul Heese Gerhard Kircher Thomas Kleinert Thorsten Koch Georgios Korpas Steve Lenk Jakub Marecek Vanio Markov Guglielmo Mazzola Stefano Mensa Naeimeh Mohseni Giacomo Nannicini Corey O\u2019Meara Elena Pe\u00f1a Tapia Sebastian Pokutta Manuel Proissl Patrick Rebentrost Emre Sahin Benjamin C. B. Symons Sabine Tornow Victor Valls Stefan Woerner Mira L. Wolf-Bauwens Jon Yard Sheir Yarkoni Dirk Zechiel Sergiy Zhuk and Christa Zoufal. 2023. Quantum Optimization: Potential Challenges and the Path Forward. arxiv:2312.02279 [quant-ph]","DOI":"10.2172\/2229681"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.8.031016"},{"key":"e_1_3_1_6_2","doi-asserted-by":"publisher","DOI":"10.3389\/fphy.2019.00048"},{"key":"e_1_3_1_7_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.16.3.538"},{"key":"e_1_3_1_8_2","doi-asserted-by":"publisher","unstructured":"Thomas Bouquet Mehdi Hmyene Fran\u00e7ois Porcher Lorenzo Pugliese and Jad Zeroual. 2021. Approximating Optimal Asset Allocations using Simulated Bifurcation. arxiv:2108.03092 [q-fin.PM]. 10.48550\/arXiv.2108.03092","DOI":"10.48550\/arXiv.2108.03092"},{"key":"e_1_3_1_9_2","doi-asserted-by":"publisher","unstructured":"Howard E. Brandt. 1999. Qubit Devices and the Issue of Quantum Decoherence. 257\u2013370 pages. 10.1016\/S0079-6727(99)00003-8","DOI":"10.1016\/S0079-6727(99)00003-8"},{"key":"e_1_3_1_10_2","doi-asserted-by":"publisher","unstructured":"Giulio Casati and Vyacheslav Girko. 1993. Wigner\u2019s semicircle law for band random matrices. (1993). 10.1515\/rose.1993.1.1.15","DOI":"10.1515\/rose.1993.1.1.15"},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2021.0419"},{"key":"e_1_3_1_12_2","doi-asserted-by":"publisher","unstructured":"Mark W. Coffey. 2017. Adiabatic Quantum Computing Solution of the Knapsack Problem. 10.48550\/arxiv.1701.05584","DOI":"10.48550\/arxiv.1701.05584"},{"key":"e_1_3_1_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.vlsi.2019.07.003"},{"key":"e_1_3_1_14_2","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2023.3312559"},{"key":"e_1_3_1_15_2","unstructured":"Alexander M. Dalzell Sam McArdle Mario Berta Przemyslaw Bienias Chi-Fang Chen Andr\u00e1s Gily\u00e9n Connor T. Hann Michael J. Kastoryano Emil T. Khabiboulline Aleksander Kubica Grant Salton Samson Wang and Fernando G. S. L. Brand\u00e3o. 2023. Quantum Algorithms: A Survey of Applications and End-to-end Complexities. arxiv:2310.03011 [quant-ph]"},{"key":"e_1_3_1_16_2","doi-asserted-by":"publisher","unstructured":"Bryan Dury and Olivia Di Matteo. 2020. A QUBO Formulation for Qubit Allocation. 10.48550\/ARXIV.2009.00140","DOI":"10.48550\/ARXIV.2009.00140"},{"key":"e_1_3_1_17_2","unstructured":"Elias F. Combarro Samuel Gonz\u00e1lez-Castillo and Alberto Di Meglio. 2023. A Practical Guide to Quantum Machine Learning and Quantum Optimization: Hands-on Approach to Modern Quantum Algorithms. Packt Publishing Ltd."},{"key":"e_1_3_1_18_2","doi-asserted-by":"publisher","unstructured":"Fred Glover Gary Kochenberger and Yu Du. 2018. A Tutorial on Formulating and Using QUBO Models. 10.48550\/arXiv.1811.11538","DOI":"10.48550\/arXiv.1811.11538"},{"key":"e_1_3_1_19_2","doi-asserted-by":"publisher","DOI":"10.1038\/srep21686"},{"key":"e_1_3_1_20_2","doi-asserted-by":"publisher","DOI":"10.7566\/JPSJ.88.061015"},{"key":"e_1_3_1_21_2","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.abe7953."},{"key":"e_1_3_1_22_2","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.aav2372"},{"key":"e_1_3_1_23_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-4-431-55756-2_12"},{"key":"e_1_3_1_24_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.92.042325"},{"key":"e_1_3_1_25_2","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.1904.12139"},{"key":"e_1_3_1_26_2","volume-title":"pyqubo","author":"Iosue Joseph T.","unstructured":"Joseph T. Iosue. n.d. pyqubo. https:\/\/github.com\/recruit-communication"},{"key":"e_1_3_1_27_2","unstructured":"Joseph T. Iosue. 2019. Qubovert Documentation. Retrieved May 10 2022 from https:\/\/qubovert.readthedocs.io\/en\/stable\/"},{"key":"e_1_3_1_28_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature10012"},{"key":"e_1_3_1_29_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.58.5355"},{"key":"e_1_3_1_30_2","doi-asserted-by":"publisher","DOI":"10.35848\/1882-0786\/acaba9"},{"key":"e_1_3_1_31_2","doi-asserted-by":"publisher","DOI":"10.1109\/ICCD.2004.1347938"},{"key":"e_1_3_1_32_2","doi-asserted-by":"publisher","DOI":"10.3390\/drones3030066"},{"key":"e_1_3_1_33_2","doi-asserted-by":"publisher","DOI":"10.1088\/2058-9565\/ac4d1b"},{"key":"e_1_3_1_34_2","doi-asserted-by":"publisher","DOI":"10.1109\/TQE.2021.3068355"},{"key":"e_1_3_1_35_2","doi-asserted-by":"publisher","DOI":"10.1109\/ISCAS48785.2022.9937557"},{"key":"e_1_3_1_36_2","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2020.2970105"},{"key":"e_1_3_1_37_2","unstructured":"Frauke Liers Tim Nieberg and Gregor Pardella. 2011. Via Minimization in VLSI Chip Design Application of a Planar Max-cut Algorithm. http:\/\/e-archive.informatik.uni-koeln.de\/630\/"},{"key":"e_1_3_1_38_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.94.022337"},{"key":"e_1_3_1_39_2","first-page":"3","article-title":"A study on updating spins in Ising model to solve combinatorial optimization problems","volume":"4","author":"Naito Yuki","unstructured":"Yuki Naito and Kunihiro Fujiyoshi. n.d. A study on updating spins in Ising model to solve combinatorial optimization problems. City 4 (n.d.), 3. https:\/\/sasimi.jp\/new\/sasimi2019\/files\/archive\/pdf\/p310_R4-13.pdf","journal-title":"City"},{"key":"e_1_3_1_40_2","volume-title":"Stochastic Benchmark Repository","author":"Usra-Riacs","unstructured":"Usra-Riacs. 2021. Stochastic Benchmark Repository. Retrieved June 3, 2023 from https:\/\/github.com\/usra-riacs\/stochastic-benchmark"},{"key":"e_1_3_1_41_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511976667"},{"key":"e_1_3_1_42_2","volume-title":"VLSI Digital Signal Processing Systems: Design and Implementation","author":"Parhi Keshab K.","year":"1999","unstructured":"Keshab K. Parhi. 1999. VLSI Digital Signal Processing Systems: Design and Implementation. John Wiley & Sons."},{"key":"e_1_3_1_43_2","volume-title":"Characterizing and Benchmarking QUBO Reformulations of the Knapsack Problem","author":"Quintero Rodolfo A.","year":"2021","unstructured":"Rodolfo A. Quintero and Luis F. Zuluaga. 2021. Characterizing and Benchmarking QUBO Reformulations of the Knapsack Problem. Technical Report. Department of Industrial and Systems Engineering, Lehigh University."},{"key":"e_1_3_1_44_2","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2021.0417"},{"key":"e_1_3_1_45_2","doi-asserted-by":"publisher","DOI":"10.1145\/3474223"},{"key":"e_1_3_1_46_2","doi-asserted-by":"publisher","unstructured":"Stefano Speziali Federico Bianchi Andrea Marini Lorenzo Menculini Massimiliano Proietti Loris F. Termite Alberto Garinei Marcello Marconi and Andrea Delogu. 2021. Solving Sensor Placement Problems in Real Water Distribution Networks Using Adiabatic Quantum Computation. 10.48550\/arxiv.2108.04075","DOI":"10.48550\/arxiv.2108.04075"},{"key":"e_1_3_1_47_2","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2009.08412"},{"key":"e_1_3_1_48_2","doi-asserted-by":"publisher","DOI":"10.1109\/FCCM.2007.56"},{"key":"e_1_3_1_49_2","doi-asserted-by":"publisher","unstructured":"Toufan D. Tambunan Andriyan B. Suksmono Ian J. M. Edward and Rahmat Mulyawan. 2022. Quantum Annealing for Vehicle Routing Problem with Weighted Segment. 10.48550\/ARXIV.2203.13469","DOI":"10.48550\/ARXIV.2203.13469"},{"key":"e_1_3_1_50_2","doi-asserted-by":"publisher","DOI":"10.7566\/JPSJ.88.061010"},{"key":"e_1_3_1_51_2","doi-asserted-by":"publisher","DOI":"10.1145\/3468044.3468045"},{"key":"e_1_3_1_52_2","doi-asserted-by":"publisher","DOI":"10.1109\/FPL.2019.00019"},{"key":"e_1_3_1_53_2","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2023.3316727"},{"key":"e_1_3_1_54_2","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2023.3326816"},{"key":"e_1_3_1_55_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41928-021-00546-4"},{"key":"e_1_3_1_56_2","volume-title":"Classical Mechanics","author":"Taylor John Robert","year":"2005","unstructured":"John Robert Taylor and John R. Taylor. 2005. Classical Mechanics. Vol. 1. Springer."},{"key":"e_1_3_1_57_2","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.76.1037"},{"key":"e_1_3_1_58_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.5.031040"},{"key":"e_1_3_1_59_2","doi-asserted-by":"publisher","unstructured":"Amit Verma and Mark Lewis. 2021. Variable Reduction For Quadratic Unconstrained Binary Optimization. 10.48550\/arxiv.2105.07032","DOI":"10.48550\/arxiv.2105.07032"},{"key":"e_1_3_1_60_2","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2023.3260765"},{"key":"e_1_3_1_61_2","doi-asserted-by":"publisher","DOI":"10.5120\/3084-4222"},{"key":"e_1_3_1_62_2","unstructured":"Pedro Maciel Xavier Pedro Ripper Tiago Andrade Joaquim Dias Garcia Nelson Maculan and David E. Bernal Neira. 2023. QUBO.jl: A Julia Ecosystem for Quadratic Unconstrained Binary Optimization. arxiv:2307.02577 [math.OC]"},{"key":"e_1_3_1_63_2","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2021.3063618"},{"key":"e_1_3_1_64_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-50743-5_10"},{"key":"e_1_3_1_65_2","doi-asserted-by":"publisher","DOI":"10.23919\/DATE54114.2022.9774576"},{"key":"e_1_3_1_66_2","doi-asserted-by":"publisher","DOI":"10.1109\/ISOCC53507.2021.9613918"},{"key":"e_1_3_1_67_2","doi-asserted-by":"publisher","DOI":"10.1109\/FPT.2009.5377620"},{"key":"e_1_3_1_68_2","doi-asserted-by":"publisher","DOI":"10.1145\/1046192.1046202"},{"key":"e_1_3_1_69_2","doi-asserted-by":"publisher","DOI":"10.1145\/3492805.3492815"},{"key":"e_1_3_1_70_2","doi-asserted-by":"publisher","DOI":"10.1145\/3373087.3375298"}],"container-title":["ACM Transactions on Quantum Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3665281","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3665281","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T00:58:34Z","timestamp":1750294714000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3665281"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,14]]},"references-count":69,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,3,31]]}},"alternative-id":["10.1145\/3665281"],"URL":"https:\/\/doi.org\/10.1145\/3665281","relation":{},"ISSN":["2643-6809","2643-6817"],"issn-type":[{"value":"2643-6809","type":"print"},{"value":"2643-6817","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1,14]]},"assertion":[{"value":"2023-09-27","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-04-26","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-01-14","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}