{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T03:15:46Z","timestamp":1778901346586,"version":"3.51.4"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2024,7,1]],"date-time":"2024-07-01T00:00:00Z","timestamp":1719792000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,7,1]],"date-time":"2024-07-01T00:00:00Z","timestamp":1719792000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100002744","name":"Bar-Ilan University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100002744","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Mach. Intell."],"published-print":{"date-parts":[[2024,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The quantum approximate optimization algorithm (QAOA) is a leading iterative variational quantum algorithm for heuristically solving combinatorial optimization problems. A large portion of the computational effort in QAOA is spent by the optimization steps, which require many executions of the quantum circuit. Therefore, there is active research focusing on finding better initial circuit parameters, which would reduce the number of required iterations and hence the overall execution time. While existing methods for parameter initialization have shown great success, they often offer a single set of parameters for all problem instances. We propose a practical method that uses a simple, fully connected neural network that leverages previous executions of QAOA to find better initialization parameters tailored to a new given problem instance. We benchmark state-of-the-art initialization methods for solving the MaxCut problem of Erd\u0151s-R\u00e9nyi graphs using QAOA and show that our method is consistently the fastest to converge while also yielding the best final result. Furthermore, the parameters predicted by the neural network are shown to match very well with the fully optimized parameters, to the extent that no iterative steps are required, thereby effectively realizing an iteration-free QAOA scheme.<\/jats:p>","DOI":"10.1007\/s42484-024-00159-y","type":"journal-article","created":{"date-parts":[[2024,7,1]],"date-time":"2024-07-01T22:02:01Z","timestamp":1719871321000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Iteration-Free quantum approximate optimization algorithm using neural networks"],"prefix":"10.1007","volume":"6","author":[{"given":"Ohad","family":"Amosy","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tamuz","family":"Danzig","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ohad","family":"Lev","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ely","family":"Porat","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gal","family":"Chechik","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Adi","family":"Makmal","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,7,1]]},"reference":[{"issue":"1","key":"159_CR1","doi-asserted-by":"publisher","first-page":"010401","DOI":"10.1103\/PhysRevA.104.L010401","volume":"104","author":"V Akshay","year":"2021","unstructured":"Akshay V, Rabinovich D, Campos E, Biamonte J (2021) Parameter concentrations in quantum approximate optimization. Phys Rev A 104(1):010401","journal-title":"Phys Rev A"},{"key":"159_CR2","doi-asserted-by":"crossref","unstructured":"Alam M, Ash-Saki A, Ghosh S (2020) Accelerating quantum approximate optimization algorithm using machine learning. In: 2020 Design, Automation & Test in Europe Conference & Exhibition (DATE), IEEE, pp 686\u2013689","DOI":"10.23919\/DATE48585.2020.9116348"},{"key":"159_CR3","unstructured":"Aleksandrowicz G, Alexander T, Barkoutsos P, Bello L, Ben-Haim Y, Bucher D, Cabrera-Hern\u00e1ndez FJ, Carballo-Franquis J, Chen A, Chen C-F et al (2019) Qiskit: an open-source framework for quantum computing. 16"},{"key":"159_CR4","doi-asserted-by":"crossref","unstructured":"Amosy O, Chechik G (2022) Coupled training for multi-source domain adaptation. In: Proceedings of the IEEE\/CVF winter conference on applications of computer vision, pp 420\u2013429","DOI":"10.1109\/WACV51458.2022.00114"},{"key":"159_CR5","doi-asserted-by":"crossref","unstructured":"Amosy O, Eyal G, Chechik G (2024) Late to the party? On-demand unlabeled personalized federated learning. In: Proceedings of the IEEE\/CVF winter conference on applications of computer vision, pp 2184\u20132193","DOI":"10.1109\/WACV57701.2024.00218"},{"key":"159_CR6","unstructured":"Amosy O, Volk T, Ben-David E, Reichart R, Chechik G (2022) Text2Model: model induction for zero-shot generalization using task descriptions. arXiv:2210.15182"},{"key":"159_CR7","unstructured":"Barak B, Marwaha K (2021) Classical algorithms and quantum limitations for maximum cut on high-girth graphs. arXiv:2106.05900"},{"key":"159_CR8","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1007\/s10994-009-5152-4","volume":"79","author":"S Ben-David","year":"2010","unstructured":"Ben-David S, Blitzer J, Crammer K, Kulesza A, Pereira F, Vaughan JW (2010) A theory of learning from different domains. Mach Learn 79:151\u2013175","journal-title":"Mach Learn"},{"key":"159_CR9","unstructured":"Brandao FG, Broughton M, Farhi E, Gutmann S, Neven H (2018) For fixed control parameters the quantum approximate optimization algorithm\u2019s objective function value concentrates for typical instances. arXiv:1812.04170"},{"issue":"1","key":"159_CR10","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1093\/imamat\/6.1.76","volume":"6","author":"CG Broyden","year":"1970","unstructured":"Broyden CG (1970) The convergence of a class of double-rank minimization algorithms 1. general considerations. IMA J Appl Math 6(1):76\u201390","journal-title":"IMA J Appl Math"},{"issue":"9","key":"159_CR11","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1038\/s42254-021-00348-9","volume":"3","author":"M Cerezo","year":"2021","unstructured":"Cerezo M, Arrasmith A, Babbush R, Benjamin SC, Endo S, Fujii K, McClean JR, Mitarai K, Yuan X, Cincio L et al (2021) Variational quantum algorithms. Nat Rev Phys 3(9):625\u2013644","journal-title":"Nat Rev Phys"},{"key":"159_CR12","doi-asserted-by":"crossref","unstructured":"Conn AR, Scheinberg K, Vicente LN (2009) Introduction to derivative-free optimization. SIAM","DOI":"10.1137\/1.9780898718768"},{"key":"159_CR13","unstructured":"Crooks GE (2018) Performance of the quantum approximate optimization algorithm on the maximum cut problem. arXiv:1811.08419"},{"key":"159_CR14","doi-asserted-by":"publisher","first-page":"479","DOI":"10.22331\/q-2021-06-17-479","volume":"5","author":"DJ Egger","year":"2021","unstructured":"Egger DJ, Mare\u010dek J, Woerner S (2021) Warm-starting quantum optimization. Quantum 5:479","journal-title":"Quantum"},{"key":"159_CR15","unstructured":"Farhi E, Goldstone J, Gutmann S (2014) A quantum approximate optimization algorithm. arXiv:1411.4028"},{"key":"159_CR16","unstructured":"Farhi E, Goldstone J, Gutmann S, Sipser M (2000) Quantum computation by adiabatic evolution"},{"key":"159_CR17","unstructured":"Farhi E, Harrow AW (2016) Quantum supremacy through the quantum approximate optimization algorithm. arXiv:1602.07674"},{"issue":"3","key":"159_CR18","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1093\/comjnl\/13.3.317","volume":"13","author":"R Fletcher","year":"1970","unstructured":"Fletcher R (1970) A new approach to variable metric algorithms. Comput J 13(3):317\u2013322","journal-title":"Comput J"},{"issue":"4","key":"159_CR19","doi-asserted-by":"publisher","first-page":"042433","DOI":"10.1103\/PhysRevA.106.042433","volume":"106","author":"L Friedrich","year":"2022","unstructured":"Friedrich L, Maziero J (2022) Avoiding barren plateaus with classical deep neural networks. Phys Rev A 106(4):042433","journal-title":"Phys Rev A"},{"issue":"2","key":"159_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s42979-020-00437-z","volume":"2","author":"FG Fuchs","year":"2021","unstructured":"Fuchs FG, Kolden H\u00d8, Aase NH, Sartor G (2021) Efficient encoding of the weighted max $$k$$-cut on a quantum computer using QAOA. SN Comput Sci 2(2):1\u201314","journal-title":"SN Comput Sci"},{"key":"159_CR21","doi-asserted-by":"crossref","unstructured":"Galda A, Liu X, Lykov D, Alexeev Y, Safro I (2021) Transferability of optimal QAOA parameters between random graphs. In: 2021 IEEE International conference on quantum computing and engineering (QCE), IEEE, pp 171\u2013180","DOI":"10.1109\/QCE52317.2021.00034"},{"key":"159_CR22","doi-asserted-by":"crossref","unstructured":"Gily\u00e9n A, Arunachalam S, Wiebe N (2019) Optimizing quantum optimization algorithms via faster quantum gradient computation. In: Proceedings of the thirtieth annual ACM-SIAM symposium on discrete algorithms, SIAM, pp 1425\u20131444","DOI":"10.1137\/1.9781611975482.87"},{"issue":"109","key":"159_CR23","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1090\/S0025-5718-1970-0258249-6","volume":"24","author":"D Goldfarb","year":"1970","unstructured":"Goldfarb D (1970) A family of variable-metric methods derived by variational means. Math Comput 24(109):23\u201326","journal-title":"Math Comput"},{"key":"159_CR24","doi-asserted-by":"crossref","unstructured":"Jain N, Coyle B, Kashefi E, Kumar N (2021) Graph neural network initialisation of quantum approximate optimisation. arXiv:2111.03016","DOI":"10.22331\/q-2022-11-17-861"},{"key":"159_CR25","unstructured":"Khairy S, Shaydulin R, Cincio L, Alexeev Y, Balaprakash P (2019) Reinforcement learning for quantum approximate optimization. Research Poster, accepted at Supercomputing 19"},{"key":"159_CR26","doi-asserted-by":"crossref","unstructured":"Khairy S, Shaydulin R, Cincio L, Alexeev Y, Balaprakash P (2019) Reinforcement-learning-based variational quantum circuits optimization for combinatorial problems. arXiv:1911.04574","DOI":"10.1609\/aaai.v34i03.5616"},{"key":"159_CR27","doi-asserted-by":"crossref","unstructured":"Khairy S, Shaydulin R, Cincio L, Alexeev Y, Balaprakash P (2020) Learning to optimize variational quantum circuits to solve combinatorial problems. In: Proceedings of the AAAI conference on artificial intelligence, vol 34, pp 2367\u20132375","DOI":"10.1609\/aaai.v34i03.5616"},{"key":"159_CR28","doi-asserted-by":"crossref","unstructured":"Korte BH, Vygen J, Korte B, Vygen J (2011) Combinatorial optimization vol 1","DOI":"10.1007\/978-3-642-24488-9_1"},{"key":"159_CR29","doi-asserted-by":"crossref","unstructured":"Lotshaw PC, Nguyen T, Santana A, McCaskey A, Herrman R, Ostrowski J, Siopsis G, Humble TS (2022) Scaling quantum approximate optimization on near-term hardware. arXiv:2201.02247","DOI":"10.1038\/s41598-022-14767-w"},{"issue":"4","key":"159_CR30","doi-asserted-by":"publisher","first-page":"042308","DOI":"10.1103\/PhysRevA.95.042308","volume":"95","author":"JR McClean","year":"2017","unstructured":"McClean JR, Kimchi-Schwartz ME, Carter J, De Jong WA (2017) Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states. Phys Rev A 95(4):042308","journal-title":"Phys Rev A"},{"issue":"3","key":"159_CR31","doi-asserted-by":"publisher","first-page":"032309","DOI":"10.1103\/PhysRevA.98.032309","volume":"98","author":"K Mitarai","year":"2018","unstructured":"Mitarai K, Negoro M, Kitagawa M, Fujii K (2018) Quantum circuit learning. Phys Rev A 98(3):032309","journal-title":"Phys Rev A"},{"issue":"1","key":"159_CR32","doi-asserted-by":"publisher","first-page":"013304","DOI":"10.1103\/PhysRevE.99.013304","volume":"99","author":"G Nannicini","year":"2019","unstructured":"Nannicini G (2019) Performance of hybrid quantum-classical variational heuristics for combinatorial optimization. Phys Rev E 99(1):013304","journal-title":"Phys Rev E"},{"key":"159_CR33","doi-asserted-by":"publisher","first-page":"79","DOI":"10.22331\/q-2018-08-06-79","volume":"2","author":"J Preskill","year":"2018","unstructured":"Preskill J (2018) Quantum computing in the NISQ era and beyond. Quantum 2:79","journal-title":"Quantum"},{"issue":"15","key":"159_CR34","doi-asserted-by":"publisher","first-page":"2601","DOI":"10.3390\/math10152601","volume":"10","author":"D Rabinovich","year":"2022","unstructured":"Rabinovich D, Sengupta R, Campos E, Akshay V, Biamonte J (2022) Progress towards analytically optimal angles in quantum approximate optimisation. Mathematics 10(15):2601","journal-title":"Mathematics"},{"key":"159_CR35","doi-asserted-by":"crossref","unstructured":"Sack SH, Serbyn M (2021) Quantum annealing initialization of the quantum approximate optimization algorithm. arXiv:2101.05742","DOI":"10.22331\/q-2021-07-01-491"},{"issue":"3","key":"159_CR36","doi-asserted-by":"publisher","first-page":"032331","DOI":"10.1103\/PhysRevA.99.032331","volume":"99","author":"M Schuld","year":"2019","unstructured":"Schuld M, Bergholm V, Gogolin C, Izaac J, Killoran N (2019) Evaluating analytic gradients on quantum hardware. Phys Rev A 99(3):032331","journal-title":"Phys Rev A"},{"issue":"111","key":"159_CR37","doi-asserted-by":"publisher","first-page":"647","DOI":"10.1090\/S0025-5718-1970-0274029-X","volume":"24","author":"DF Shanno","year":"1970","unstructured":"Shanno DF (1970) Conditioning of quasi-newton methods for function minimization. Math Comput 24(111):647\u2013656","journal-title":"Math Comput"},{"key":"159_CR38","doi-asserted-by":"crossref","unstructured":"Shaydulin R, Safro I, Larson J (2019) Multistart methods for quantum approximate optimization. In: 2019 IEEE High performance extreme computing conference (HPEC), IEEE, pp 1\u20138","DOI":"10.1109\/HPEC.2019.8916288"},{"key":"159_CR39","unstructured":"Spirakis P, Nikoletseas S, Raptopoulos C (2021) Max cut in weighted random intersection graphs and discrepancy of sparse random set systems. LIPIcs: Leibniz International proceedings in informatics"},{"key":"159_CR40","unstructured":"Sturm A (2023) Theory and implementation of the quantum approximate optimization algorithm: a comprehensible introduction and case study using Qiskit and IBM Quantum computers. arXiv:2301.09535"},{"key":"159_CR41","unstructured":"Verdon G, Broughton M, McClean JR, Sung KJ, Babbush R, Jiang Z, Neven H, Mohseni M (2019) Learning to learn with quantum neural networks via classical neural networks. arXiv:1907.05415"},{"key":"159_CR42","doi-asserted-by":"crossref","unstructured":"Volk T, Ben-David E, Amosy O, Chechik G, Reichart R (2023) Example-based hypernetworks for multi-source adaptation to unseen domains. In: Findings of the association for computational linguistics: EMNLP 2023, pp 9096\u20139113","DOI":"10.18653\/v1\/2023.findings-emnlp.610"},{"key":"159_CR43","doi-asserted-by":"crossref","unstructured":"Wang H, Zhao J, Wang B, Tong L (2021) A quantum approximate optimization algorithm with metalearning for MaxCut problem and its simulation via tensorflow quantum. Math Probl Eng 2021","DOI":"10.1155\/2021\/6655455"},{"issue":"3","key":"159_CR44","first-page":"033446","volume":"2","author":"MM Wauters","year":"2020","unstructured":"Wauters MM, Panizon E, Mbeng GB, Santoro GE (2020) Reinforcement-learning-assisted quantum optimization. Phys Rev Phys 2(3):033446","journal-title":"Phys Rev Phys"},{"key":"159_CR45","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11128-020-02692-8","volume":"19","author":"M Willsch","year":"2020","unstructured":"Willsch M, Willsch D, Jin F, De Raedt H, Michielsen K (2020) Benchmarking the quantum approximate optimization algorithm. Quantum Inf Process 19:1\u201324","journal-title":"Quantum Inf Process"},{"issue":"1","key":"159_CR46","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s42484-020-00022-w","volume":"3","author":"M Wilson","year":"2021","unstructured":"Wilson M, Stromswold R, Wudarski F, Hadfield S, Tubman NM, Rieffel EG (2021) Optimizing quantum heuristics with meta-learning. Quantum Mach Intell 3(1):1\u201314","journal-title":"Quantum Mach Intell"},{"issue":"2","key":"159_CR47","first-page":"021067","volume":"10","author":"L Zhou","year":"2020","unstructured":"Zhou L, Wang S-T, Choi S, Pichler H, Lukin MD (2020) Quantum approximate optimization algorithm: performance, mechanism, and implementation on near-term devices. Phys Rev X 10(2):021067","journal-title":"Phys Rev X"}],"container-title":["Quantum Machine Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42484-024-00159-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s42484-024-00159-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42484-024-00159-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,23]],"date-time":"2024-12-23T16:03:47Z","timestamp":1734969827000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s42484-024-00159-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,1]]},"references-count":47,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,12]]}},"alternative-id":["159"],"URL":"https:\/\/doi.org\/10.1007\/s42484-024-00159-y","relation":{},"ISSN":["2524-4906","2524-4914"],"issn-type":[{"value":"2524-4906","type":"print"},{"value":"2524-4914","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,1]]},"assertion":[{"value":"21 March 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 April 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 July 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"38"}}