{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T03:22:24Z","timestamp":1774322544270,"version":"3.50.1"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,3,26]],"date-time":"2021-03-26T00:00:00Z","timestamp":1616716800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,3,26]],"date-time":"2021-03-26T00:00:00Z","timestamp":1616716800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100006602","name":"Air Force Research Laboratory","doi-asserted-by":"publisher","award":["FA8750-18-C-0167"],"award-info":[{"award-number":["FA8750-18-C-0167"]}],"id":[{"id":"10.13039\/100006602","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Mach. Intell."],"published-print":{"date-parts":[[2021,6]]},"DOI":"10.1007\/s42484-021-00039-9","type":"journal-article","created":{"date-parts":[[2021,3,26]],"date-time":"2021-03-26T16:02:31Z","timestamp":1616774551000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Optimizing the optimizer: decomposition techniques for quantum annealing"],"prefix":"10.1007","volume":"3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0410-649X","authenticated-orcid":false,"given":"Gideon","family":"Bass","sequence":"first","affiliation":[]},{"given":"Maxwell","family":"Henderson","sequence":"additional","affiliation":[]},{"given":"Joshua","family":"Heath","sequence":"additional","affiliation":[]},{"suffix":"III","given":"Joseph","family":"Dulny","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,3,26]]},"reference":[{"issue":"607","key":"39_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.compchemeng.2019.106630","volume":"132","author":"A Ajagekar","year":"2020","unstructured":"Ajagekar A, Humble T, You F (2020) Quantum computing based hybrid solution strategies for large-scale discrete-continuous optimization problems. Comput Chem Eng 132(607):1\u201350. ISSN 00981354. https:\/\/doi.org\/10.1016\/j.compchemeng.2019.106630","journal-title":"Comput Chem Eng"},{"issue":"7779","key":"39_CR2","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1038\/s41586-019-1666-5","volume":"574","author":"F Arute","year":"2019","unstructured":"Arute F et al (2019) Quantum supremacy using a programmable superconducting processor. Nature 574(7779):505\u2013510. ISSN 14764687. https:\/\/doi.org\/10.1038\/s41586-019-1666-5","journal-title":"Nature"},{"issue":"2","key":"39_CR3","doi-asserted-by":"publisher","first-page":"24010","DOI":"10.1088\/2058-9565\/aaadc2","volume":"3","author":"G Bass","year":"2018","unstructured":"Bass G, Tomlin C, Kumar V, Rihaczek P, Dulny J (2018) Heterogeneous quantum computing for satellite constellation optimization: solving the weighted k-clique problem. Quantum Sci Technol 3 (2):24010. ISSN 2058-9565. https:\/\/doi.org\/10.1088\/2058-9565\/aaadc2","journal-title":"Quantum Sci Technol"},{"key":"39_CR4","doi-asserted-by":"publisher","first-page":"56","DOI":"10.3389\/fphy.2014.00056","volume":"2","author":"Z Bian","year":"2014","unstructured":"Bian Z, Chudak F, Israel R, Lackey B, Macready WG, Roy A (2014) Discrete optimization using quantum annealing on sparse Ising models. Front Phys 2:56. ISSN 2296-424X. https:\/\/doi.org\/10.3389\/fphy.2014.00056","journal-title":"Front Phys"},{"key":"39_CR5","doi-asserted-by":"crossref","unstructured":"Bian Z, Chudak F, Israel R, Lackey B, Macready WG, Roy A (2016) Mapping constrained optimization problems to quantum annealing with application to fault diagnosis. http:\/\/arxiv.org\/1603.03111","DOI":"10.3389\/fict.2016.00014"},{"key":"39_CR6","unstructured":"Booth M, Reinhardt SP, Roy A (2017) Partitioning optimization problems for hybrid classical\/quantum execution. www.dwavesys.com"},{"key":"39_CR7","doi-asserted-by":"publisher","first-page":"779","DOI":"10.1126\/science.284.5415.779","volume":"284","author":"J Brooke","year":"1999","unstructured":"Brooke J, Bitko D, Rosenbaum T~F, Aeppli G (1999) Quantum annealing of a disordered magnet. Science 284:779. https:\/\/doi.org\/10.1126\/science.284.5415.779","journal-title":"Science"},{"key":"39_CR8","unstructured":"Cai J, Macready W~G, Roy A (2014) A practical heuristic for finding graph minors. ArXiv e-prints"},{"issue":"3-4","key":"39_CR9","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1007\/s11265-018-1357-8","volume":"91","author":"G Chapuis","year":"2019","unstructured":"Chapuis G, Djidjev H, Hahn G, Rizk G (2019) Finding maximum cliques on the D-wave quantum annealer. J Signal Process Syst 91(3-4):363\u2013377. ISSN 1939-8018. https:\/\/doi.org\/10.1007\/s11265-018-1357-8","journal-title":"J Signal Process Syst"},{"key":"39_CR10","unstructured":"D-Wave (2018) The D-Wave 2000Q System"},{"key":"39_CR11","unstructured":"Djidjev HN, Chapuis G, Hahn G, Rizk G (2018) Efficient combinatorial optimization using quantum annealing. pp 1\u201325, http:\/\/arxiv.org\/abs\/1801.08653"},{"key":"39_CR12","doi-asserted-by":"crossref","unstructured":"Djidjev HN, Hahn G, Mniszewski SM, Negre CFA, Niklasson AMN, Sardeshmukh VB (2016) Graph partitioning methods for fast parallel quantum molecular dynamics. http:\/\/arxiv.org\/abs\/1605.01118","DOI":"10.2172\/1330079"},{"issue":"5516","key":"39_CR13","doi-asserted-by":"publisher","first-page":"472","DOI":"10.1126\/science.1057726","volume":"292","author":"E Farhi","year":"2001","unstructured":"Farhi E, Goldstone J, Gutmann S, Lapan J, Lundgren A, Preda D (2001) A quantum adiabatic evolution algorithm applied to random instances of an NP-Complete problem. Science 292(5516):472. http:\/\/science.sciencemag.org\/content\/292\/5516\/472.abstract","journal-title":"Science"},{"key":"39_CR14","doi-asserted-by":"crossref","unstructured":"Finnila A~B, Gomez M~A, Sebenik C, Stenson C, Doll J~D (1994) Quantum annealing: a new method for minimizing multidimensional functions, vol 219","DOI":"10.1016\/0009-2614(94)00117-0"},{"issue":"11","key":"39_CR15","doi-asserted-by":"publisher","first-page":"1129","DOI":"10.1002\/spe.4380211102","volume":"21","author":"TMJ Fruchterman","year":"1991","unstructured":"Fruchterman TMJ, Reingold EM (1991) Graph drawing by force-directed placement. Software: Practice and Experience 21(11):1129\u20131164. ISSN 0038-0644. https:\/\/doi.org\/10.1002\/spe.4380211102","journal-title":"Software: Practice and Experience"},{"key":"39_CR16","volume-title":"Computers and intractability; a guide to the theory of NP-completeness","author":"MR Garey","year":"1990","unstructured":"Garey MR, Johnson DS (1990) Computers and intractability; a guide to the theory of NP-completeness. W. H. Freeman & Co., New York. ISBN 0716710455"},{"issue":"2","key":"39_CR17","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1023\/A:1022602019183","volume":"3","author":"DE Goldberg","year":"1988","unstructured":"Goldberg DE, Holland JH (1988) Genetic algorithms and machine learning. Mach Learn 3(2):95\u201399. ISSN 1573-0565. https:\/\/doi.org\/10.1023\/A:1022602019183","journal-title":"Mach Learn"},{"key":"39_CR18","unstructured":"Hagberg AA, Schult DAS, Swart PJ (2008) Exploring network structure, dynamics, and function using NetworkX. In: Proceedings of the 7th python in science conference (SciPy2008)"},{"issue":"6","key":"39_CR19","doi-asserted-by":"publisher","first-page":"061009","DOI":"10.7566\/JPSJ.88.061009","volume":"88","author":"M Henderson","year":"2019","unstructured":"Henderson M, Novak J, Cook T (2019) Leveraging quantum annealing for election forecasting. J Phys Soc Japan 88(6):061009. https:\/\/doi.org\/10.7566\/JPSJ.88.061009","journal-title":"J Phys Soc Japan"},{"key":"39_CR20","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/1090.001.0001","volume-title":"Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence","author":"JH Holland","year":"1992","unstructured":"Holland JH (1992) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence, 2nd edn. MIT Press, Cambridge","edition":"2nd edn."},{"key":"39_CR21","unstructured":"Job Joshua, Adachi Steve (2020)"},{"key":"39_CR22","doi-asserted-by":"publisher","first-page":"5355","DOI":"10.1103\/PhysRevE.58.5355","volume":"58","author":"T Kadowaki","year":"1998","unstructured":"Kadowaki T, Nishimori H (1998) Quantum annealing in the transverse Ising model. Phys Rev E 58:5355\u20135363. https:\/\/doi.org\/10.1103\/PhysRevE.58.5355","journal-title":"Phys Rev E"},{"key":"39_CR23","doi-asserted-by":"publisher","first-page":"5","DOI":"10.3389\/fphy.2014.00005","volume":"2","author":"A Lucas","year":"2014","unstructured":"Lucas A (2014) Ising formulations of many NP problems. Front Phys 2:5. https:\/\/doi.org\/10.3389\/fphy.2014.00005","journal-title":"Front Phys"},{"key":"39_CR24","unstructured":"Neven H, Denchev VS, Rose G, Macready WG (2012) Qboost: Large scale classifier training with adiabatic quantum optimization. In: Hoi SCH, Buntine W (eds) Proceedings of the Asian conference on machine learning, vol 25 of proceedings of machine learning research. PMLR. http:\/\/proceedings.mlr.press\/v25\/neven12.html. Singapore Management University, Singapore, pp 333\u2013348"},{"key":"39_CR25","doi-asserted-by":"publisher","first-page":"034034","DOI":"10.1103\/PhysRevApplied.14.034034","volume":"14","author":"M Noori","year":"2020","unstructured":"Noori M, Vedaie SS, Singh I, Crawford D, Oberoi JS, Sanders BC, Zahedinejad E (2020) Analog-quantum feature mapping for machine-learning applications. Phys Rev Appl 14:034034. https:\/\/doi.org\/10.1103\/PhysRevApplied.14.034034","journal-title":"Phys Rev Appl"},{"key":"39_CR26","doi-asserted-by":"publisher","unstructured":"Preskill J (2018) Quantum Computing in the NISQ era and beyond. https:\/\/doi.org\/10.22331\/q-2018-08-06-79. arXiv:1801.00862","DOI":"10.22331\/q-2018-08-06-79"},{"key":"39_CR27","first-page":"1","volume":"338","author":"G Reinelt","year":"1995","unstructured":"Reinelt G (1995) Tsplib 95. interdisziplin\u00e4res Zentrum f\u00fcr Wissenschaftliches Rechnen (IWR). Heidelberg 338:1\u201316","journal-title":"Heidelberg"},{"issue":"3","key":"39_CR28","doi-asserted-by":"publisher","first-page":"448","DOI":"10.1109\/CVPRW.2009.5206577","volume":"1","author":"R Salakhutdinov","year":"2009","unstructured":"Salakhutdinov R, Hinton G (2009) Deep Boltzmann machines. Aistats 1(3):448\u2013455. ISSN 1063-6919. https:\/\/doi.org\/10.1109\/CVPRW.2009.5206577","journal-title":"Aistats"},{"key":"39_CR29","doi-asserted-by":"publisher","first-page":"2427","DOI":"10.1126\/science.1068774","volume":"295","author":"G~E Santoro","year":"2002","unstructured":"Santoro G~E, Marto\\v n\u00e1k R , Tosatti E, Car R (2002) Theory of quantum annealing of an Ising spin glass. Science 295:2427\u20132430. https:\/\/doi.org\/10.1126\/science.1068774","journal-title":"Science"},{"issue":"36","key":"39_CR30","doi-asserted-by":"publisher","first-page":"R393","DOI":"10.1088\/0305-4470\/39\/36\/R01","volume":"39","author":"GE Santoro","year":"2006","unstructured":"Santoro GE, Tosatti E (2006) Optimization using quantum mechanics: quantum annealing through adiabatic evolution. J Phys A: Math Gen 39(36):R393. http:\/\/stacks.iop.org\/0305-4470\/39\/i=36\/a=R01","journal-title":"J Phys A: Math Gen"},{"issue":"8","key":"39_CR31","doi-asserted-by":"publisher","first-page":"1675","DOI":"10.1007\/s11590-014-0814-y","volume":"9","author":"RR Squires","year":"2014","unstructured":"Squires RR, Hoffman KL (2014) A military maintenance planning and scheduling problem. Optim Lett 9(8):1675\u20131688. ISSN 18624480. https:\/\/doi.org\/10.1007\/s11590-014-0814-y","journal-title":"Optim Lett"}],"container-title":["Quantum Machine Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42484-021-00039-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s42484-021-00039-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42484-021-00039-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,22]],"date-time":"2022-12-22T15:32:16Z","timestamp":1671723136000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s42484-021-00039-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,26]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["39"],"URL":"https:\/\/doi.org\/10.1007\/s42484-021-00039-9","relation":{},"ISSN":["2524-4906","2524-4914"],"issn-type":[{"value":"2524-4906","type":"print"},{"value":"2524-4914","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,26]]},"assertion":[{"value":"27 July 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 January 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 March 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"10"}}