{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T03:18:51Z","timestamp":1778037531197,"version":"3.51.4"},"reference-count":56,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,7,17]],"date-time":"2023-07-17T00:00:00Z","timestamp":1689552000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,7,17]],"date-time":"2023-07-17T00:00:00Z","timestamp":1689552000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100002911","name":"Universidad Complutense de Madrid","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100002911","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":[[2023,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The efficient resolution of optimization problems is one of the key issues in today\u2019s industry. This task relies mainly on classical algorithms that present scalability problems and processing limitations. Quantum computing has emerged to challenge these types of problems. In this paper, we focus on the Metropolis-Hastings quantum algorithm, which is based on quantum walks. We use this algorithm to build a quantum software tool called Quantum Metropolis Solver (QMS). We validate QMS with the N-Queen problem to show a potential quantum advantage in an example that can be easily extrapolated to an Artificial Intelligence domain. We carry out different simulations to validate the performance of QMS and its configuration.<\/jats:p>","DOI":"10.1007\/s42484-023-00119-y","type":"journal-article","created":{"date-parts":[[2023,7,17]],"date-time":"2023-07-17T13:01:37Z","timestamp":1689598897000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Quantum Metropolis Solver: a quantum walks approach to optimization problems"],"prefix":"10.1007","volume":"5","author":[{"given":"Roberto","family":"Campos","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P. A. M.","family":"Casares","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. A.","family":"Martin-Delgado","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,7,17]]},"reference":[{"key":"119_CR1","doi-asserted-by":"crossref","unstructured":"Bretthauer KM, Shetty B (2002) The nonlinear knapsack problem\u2013algorithms and applications, European Journal of Operational Research, vol.\u00a0138, no.\u00a03, pp.\u00a0459\u2013472","DOI":"10.1016\/S0377-2217(01)00179-5"},{"key":"119_CR2","doi-asserted-by":"crossref","unstructured":"Hoffman KL, Padberg M, Rinaldi G, et\u00a0al (2013) Traveling salesman problem, Encyclopedia of operations research and management science, vol.\u00a01, pp.\u00a01573\u20131578","DOI":"10.1007\/978-1-4419-1153-7_1068"},{"issue":"8","key":"119_CR3","doi-asserted-by":"publisher","first-page":"1232","DOI":"10.1016\/j.trb.2011.02.004","volume":"45","author":"T Bekta\u015f","year":"2011","unstructured":"Bekta\u015f T, Laporte G (2011) The pollution-routing problem. Transportation Research Part B: Methodological 45(8):1232\u20131250","journal-title":"Transportation Research Part B: Methodological"},{"issue":"10","key":"119_CR4","doi-asserted-by":"publisher","first-page":"767","DOI":"10.1073\/pnas.42.10.767","volume":"42","author":"R Bellman","year":"1956","unstructured":"Bellman R (1956) Dynamic programming and lagrange multipliers. Proceedings of the National Academy of Sciences 42(10):767\u2013769","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"119_CR5","doi-asserted-by":"crossref","unstructured":"Kumar SN,\u00a0Panneerselvam R (2012) A survey on the vehicle routing problem and its variants, Intelligent Information Management, 2012","DOI":"10.4236\/iim.2012.43010"},{"issue":"4","key":"119_CR6","doi-asserted-by":"publisher","first-page":"667","DOI":"10.1137\/S0036144503423264","volume":"46","author":"S Boyd","year":"2004","unstructured":"Boyd S, Diaconis P, Xiao L (2004) Fastest mixing Markov chain on a graph. SIAM review 46(4):667\u2013689","journal-title":"SIAM review"},{"issue":"3","key":"119_CR7","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1016\/S0377-2217(01)00179-5","volume":"138","author":"KM Bretthauer","year":"2002","unstructured":"Bretthauer KM, Shetty B (2002) The nonlinear knapsack problem-algorithms and applications. European Journal of Operational Research 138(3):459\u2013472","journal-title":"European Journal of Operational Research"},{"issue":"49","key":"119_CR8","doi-asserted-by":"publisher","first-page":"17408","DOI":"10.1073\/pnas.1408184111","volume":"111","author":"B Calderhead","year":"2014","unstructured":"Calderhead B (2014) A general construction for parallelizing Metropolis-Hastings algorithms. Proceedings of the National Academy of Sciences 111(49):17408\u201317413","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"2","key":"119_CR9","doi-asserted-by":"publisher","DOI":"10.1088\/2058-9565\/ac4f2f","volume":"7","author":"PAM Casares","year":"2022","unstructured":"Casares PAM, Campos R, Martin-Delgado MA (2022) Qfold: quantum walks and deep learning to solve protein folding. Quantum Science and Technology 7(2):025013","journal-title":"Quantum Science and Technology"},{"key":"119_CR10","doi-asserted-by":"crossref","unstructured":"R.\u00a0Bellman, Dynamic programming and Lagrange multipliers, Proceedings of the National Academy of Sciences, vol.\u00a042, no.\u00a010, pp.\u00a0767\u2013769, 1956","DOI":"10.1073\/pnas.42.10.767"},{"key":"119_CR11","unstructured":"F.\u00a0Y. Kuo and I.\u00a0H. Sloan, Lifting the curse of dimensionality, Notices of the AMS, vol.\u00a052, no.\u00a011, pp.\u00a01320\u20131328, 2005"},{"issue":"10","key":"119_CR12","doi-asserted-by":"publisher","first-page":"2230","DOI":"10.1103\/PhysRevD.30.2230","volume":"30","author":"G Daniell","year":"1984","unstructured":"Daniell G, Hey AJ, Mandula J (1984) Error analysis for correlated Monte Carlo data. Physical Review D 30(10):2230","journal-title":"Physical Review D"},{"key":"119_CR13","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/j.trb.2012.11.002","volume":"48","author":"G Fl\u00f6tter\u00f6d","year":"2013","unstructured":"Fl\u00f6tter\u00f6d G, Bierlaire M (2013) Metropolis-Hastings sampling of paths. Transportation Research Part B: Methodological 48:53\u201366","journal-title":"Transportation Research Part B: Methodological"},{"key":"119_CR14","doi-asserted-by":"crossref","unstructured":"Galindo A, Martin-Delgado MA (2000) Family of Grover\u2019s quantum-searching algorithms. Physical Review A 62(6):062303","DOI":"10.1103\/PhysRevA.62.062303"},{"key":"119_CR15","doi-asserted-by":"publisher","first-page":"815","DOI":"10.1613\/jair.5512","volume":"59","author":"IP Gent","year":"2017","unstructured":"Gent IP, Jefferson C, Nightingale P (2017) Complexity of N-queens completion. Journal of Artificial Intelligence Research 59:815\u2013848","journal-title":"Journal of Artificial Intelligence Research"},{"issue":"2","key":"119_CR16","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1103\/PhysRevLett.79.325","volume":"79","author":"LK Grover","year":"1997","unstructured":"Grover LK (1997) Quantum mechanics helps in searching for a needle in a haystack. Physical Review Letters 79(2):325","journal-title":"Physical Review Letters"},{"key":"119_CR17","doi-asserted-by":"crossref","unstructured":"Daniell G, Hey AJ,\u00a0Mandula J (1984) Error analysis for correlated Monte Carlo data, Physical Review D, vol.\u00a030, no.\u00a010, p.\u00a02230","DOI":"10.1103\/PhysRevD.30.2230"},{"key":"119_CR18","doi-asserted-by":"crossref","unstructured":"Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing, Science, vol.\u00a0220, no.\u00a04598, pp.\u00a0671\u2013680","DOI":"10.1126\/science.220.4598.671"},{"key":"119_CR19","doi-asserted-by":"publisher","first-page":"1573","DOI":"10.1007\/978-1-4419-1153-7_1068","volume":"1","author":"KL Hoffman","year":"2013","unstructured":"Hoffman KL, Padberg M, Rinaldi G et al (2013) Traveling salesman problem. Encyclopedia of operations research and management science 1:1573\u20131578","journal-title":"Encyclopedia of operations research and management science"},{"issue":"1\u20133","key":"119_CR20","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/S0012-365X(03)00176-6","volume":"277","author":"J Hsiang","year":"2004","unstructured":"Hsiang J, Hsu DF, Shieh Y-P (2004) On the hardness of counting problems of complete mappings. Discrete mathematics 277(1\u20133):87\u2013100","journal-title":"Discrete mathematics"},{"key":"119_CR21","doi-asserted-by":"crossref","unstructured":"Kadian K, Garhwal S, Kumar A (2021) Quantum walk and its application domains: a systematic review. Computer Science Review 41:100419","DOI":"10.1016\/j.cosrev.2021.100419"},{"key":"119_CR22","doi-asserted-by":"crossref","unstructured":"Ambainis A (2004) Quantum walk algorithm for element distinctness, in Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, FOCS \u201904, (USA), p.\u00a022-31, IEEE Computer Society","DOI":"10.1109\/FOCS.2004.54"},{"issue":"4598","key":"119_CR23","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1126\/science.220.4598.671","volume":"220","author":"S Kirkpatrick","year":"1983","unstructured":"Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671\u2013680","journal-title":"Science"},{"key":"119_CR24","doi-asserted-by":"crossref","unstructured":"Temme K, Osborne TJ, Vollbrecht KG,\u00a0Poulin D,\u00a0Verstraete F (2011) Quantum metropolis sampling, Nature, vol.\u00a0471, no.\u00a07336, pp.\u00a087\u201390","DOI":"10.1038\/nature09770"},{"issue":"2","key":"119_CR25","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1006\/inco.1994.1100","volume":"115","author":"PG Kolaitis","year":"1994","unstructured":"Kolaitis PG, Thakur MN (1994) Logical definability of NP optimization problems. Information and Computation 115(2):321\u2013353","journal-title":"Information and Computation"},{"issue":"12","key":"119_CR26","doi-asserted-by":"publisher","first-page":"1011","DOI":"10.1002\/prot.25823","volume":"87","author":"A Kryshtafovych","year":"2019","unstructured":"Kryshtafovych A, Schwede T, Topf M, Fidelis K, Moult J (2019) Critical assessment of methods of protein structure prediction (CASP)-round xiii, Proteins: Structure. Function, and Bioinformatics 87(12):1011\u20131020","journal-title":"Function, and Bioinformatics"},{"key":"119_CR27","doi-asserted-by":"crossref","unstructured":"Kumar SN, Panneerselvam R (2012) A survey on the vehicle routing problem and its variants, Intelligent Information Management, 2012","DOI":"10.4236\/iim.2012.43010"},{"issue":"11","key":"119_CR28","first-page":"1320","volume":"52","author":"FY Kuo","year":"2005","unstructured":"Kuo FY, Sloan IH (2005) Lifting the curse of dimensionality. Notices of the AMS 52(11):1320\u20131328","journal-title":"Notices of the AMS"},{"key":"119_CR29","doi-asserted-by":"publisher","first-page":"287","DOI":"10.22331\/q-2020-06-29-287","volume":"4","author":"J Lemieux","year":"2020","unstructured":"Lemieux J, Heim B, Poulin D, Svore K, Troyer M (2020) Efficient quantum walk circuits for Metropolis-Hastings algorithm. Quantum 4:287","journal-title":"Quantum"},{"key":"119_CR30","doi-asserted-by":"publisher","first-page":"163","DOI":"10.22331\/q-2019-07-12-163","volume":"3","author":"GH Low","year":"2019","unstructured":"Low GH, Chuang IL (2019) Hamiltonian simulation by qubitization. Quantum 3:163","journal-title":"Quantum"},{"key":"119_CR31","doi-asserted-by":"crossref","unstructured":"Lemieux J,\u00a0Heim B,\u00a0Poulin D,\u00a0Svore K,\u00a0Troyer M (2020) Efficient quantum walk circuits for Metropolis-Hastings algorithm, Quantum, vol.\u00a04, p.\u00a0287","DOI":"10.22331\/q-2020-06-29-287"},{"issue":"1","key":"119_CR32","doi-asserted-by":"publisher","first-page":"142","DOI":"10.1137\/090745854","volume":"40","author":"F Magniez","year":"2011","unstructured":"Magniez F, Nayak A, Roland J, Santha M (2011) Search via quantum walk. SIAM journal on computing 40(1):142\u2013164","journal-title":"SIAM journal on computing"},{"key":"119_CR33","volume-title":"Portfolio selection","author":"HM Markowitz","year":"1968","unstructured":"Markowitz HM (1968) Portfolio selection. Yale University Press"},{"issue":"6","key":"119_CR34","doi-asserted-by":"publisher","first-page":"1087","DOI":"10.1063\/1.1699114","volume":"21","author":"N Metropolis","year":"1953","unstructured":"Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machines. The journal of chemical physics 21(6):1087\u20131092","journal-title":"The journal of chemical physics"},{"key":"119_CR35","volume-title":"Machine learning","author":"TM Mitchell","year":"1997","unstructured":"Mitchell TM (1997) Machine learning. McGraw-Hill, New York"},{"issue":"2181","key":"119_CR36","doi-asserted-by":"publisher","first-page":"20150301","DOI":"10.1098\/rspa.2015.0301","volume":"471","author":"A Montanaro","year":"2015","unstructured":"Montanaro A (2015) Quantum speedup of Monte Carlo methods. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471(2181):20150301","journal-title":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences"},{"key":"119_CR37","doi-asserted-by":"crossref","unstructured":"Magniez F,\u00a0Nayak A,\u00a0Roland J,\u00a0Santha M (2011) Search via quantum walk, SIAM journal on computing, vol.\u00a040, no.\u00a01, pp.\u00a0142\u2013164","DOI":"10.1137\/090745854"},{"issue":"1","key":"119_CR38","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/srep00444","volume":"2","author":"GD Paparo","year":"2012","unstructured":"Paparo GD, Martin-Delgado M (2012) Google in a quantum network. Scientific reports 2(1):1\u201312","journal-title":"Scientific reports"},{"issue":"1","key":"119_CR39","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/srep02773","volume":"3","author":"GD Paparo","year":"2013","unstructured":"Paparo GD, M\u00fcller M, Comellas F, Martin-Delgado MA (2013) Quantum google in a complex network. Scientific reports 3(1):1\u201316","journal-title":"Scientific reports"},{"issue":"3","key":"119_CR40","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.4.031002","volume":"4","author":"GD Paparo","year":"2014","unstructured":"Paparo GD, Dunjko V, Makmal A, Martin-Delgado MA, Briegel HJ (2014) Quantum speedup for active learning agents. Physical Review X 4(3):031002","journal-title":"Physical Review X"},{"key":"119_CR41","doi-asserted-by":"crossref","unstructured":"Casares PAM,\u00a0Campos R, Martin-Delgado MA (2022) Qfold: quantum walks and deep learning to solve protein folding, Quantum Science and Technology, vol.\u00a07, no.\u00a02, p.\u00a0025013","DOI":"10.1088\/2058-9565\/ac4f2f"},{"issue":"3","key":"119_CR42","doi-asserted-by":"publisher","first-page":"1041","DOI":"10.1111\/1540-6261.00453","volume":"57","author":"M Rubinstein","year":"2002","unstructured":"Rubinstein M (2002) Markowitz\u2019s portfolio selection: a fifty-year retrospective. The Journal of finance 57(3):1041\u20131045","journal-title":"The Journal of finance"},{"key":"119_CR43","doi-asserted-by":"crossref","unstructured":"Suzuki Y,\u00a0Kawase Y,\u00a0Masumura Y,\u00a0Hiraga Y,\u00a0Nakadai M,\u00a0Chen J, Nakanishi KM,\u00a0Mitarai K,\u00a0Imai R,\u00a0Tamiya S, et\u00a0al (2021) Qulacs: a fast and versatile quantum circuit simulator for research purpose, Quantum, vol.\u00a05, p.\u00a0559","DOI":"10.22331\/q-2021-10-06-559"},{"key":"119_CR44","unstructured":"Bowtell C,\u00a0Keevash P (2021) The $$ N $$-queens problem, arXiv preprint arXiv:2109.08083"},{"key":"119_CR45","unstructured":"Luria Z,\u00a0Simkin M (2021) A lower bound for the $$ N $$-queens problem, arXiv preprint arXiv:2105.11431, 2021"},{"issue":"13","key":"119_CR46","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.101.130504","volume":"101","author":"RD Somma","year":"2008","unstructured":"Somma RD, Boixo S, Barnum H, Knill E (2008) Quantum simulations of classical annealing processes. Physical Review Letters 101(13):130504","journal-title":"Physical Review Letters"},{"key":"119_CR47","doi-asserted-by":"publisher","first-page":"559","DOI":"10.22331\/q-2021-10-06-559","volume":"5","author":"Y Suzuki","year":"2021","unstructured":"Suzuki Y, Kawase Y, Masumura Y, Hiraga Y, Nakadai M, Chen J, Nakanishi KM, Mitarai K, Imai R, Tamiya S et al (2021) Qulacs: a fast and versatile quantum circuit simulator for research purpose. Quantum 5:559","journal-title":"Quantum"},{"key":"119_CR48","doi-asserted-by":"crossref","unstructured":"Crawford KD (2016) Solving the N-queens problem using genetic algorithms, in Proceedings of the 1992 ACM\/SIGAPP symposium on Applied computing: technological challenges of the 1990\u2019s, pp.\u00a01039\u20131047, 1992","DOI":"10.1145\/130069.130128"},{"key":"119_CR49","doi-asserted-by":"crossref","unstructured":"Temme K, Osborne TJ, Vollbrecht KG, Poulin D, Verstraete F (2011) Quantum metropolis sampling. Nature 471(7336):87\u201390","DOI":"10.1038\/nature09770"},{"key":"119_CR50","doi-asserted-by":"publisher","first-page":"149","DOI":"10.22331\/q-2019-06-03-149","volume":"3","author":"V Torggler","year":"2019","unstructured":"Torggler V, Aumann P, Ritsch H, Lechner W (2019) A quantum N-queens solver. Quantum 3:149","journal-title":"Quantum"},{"key":"119_CR51","doi-asserted-by":"crossref","unstructured":"Torggler V,\u00a0Aumann P,\u00a0Ritsch H,\u00a0Lechner W (2019) A quantum N-queens solver, Quantum, vol.\u00a03, p.\u00a0149","DOI":"10.22331\/q-2019-06-03-149"},{"key":"119_CR52","unstructured":"Russell S,\u00a0Norvig P (2010) Artificial Intelligence: a modern approach. Prentice Hall, 3\u00a0ed"},{"key":"119_CR53","doi-asserted-by":"crossref","unstructured":"Wolff U, Collaboration A et al (2004) Monte Carlo errors with less errors. Computer Physics Communications 156(2):143\u2013153","DOI":"10.1016\/S0010-4655(03)00467-3"},{"key":"119_CR54","unstructured":"Mitchell TM (1997) Machine learning. New York: McGraw-Hill"},{"issue":"3","key":"119_CR55","doi-asserted-by":"publisher","first-page":"754","DOI":"10.1073\/pnas.1111758109","volume":"109","author":"M-H Yung","year":"2012","unstructured":"Yung M-H, Aspuru-Guzik A (2012) A quantum-quantum metropolis algorithm. Proceedings of the National Academy of Sciences 109(3):754\u2013759","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"119_CR56","volume-title":"Random search algorithms","author":"ZB Zabinsky","year":"2009","unstructured":"Zabinsky ZB et al (2009) Random search algorithms. University of Washington, USA, Department of Industrial and Systems Engineering"}],"container-title":["Quantum Machine Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42484-023-00119-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s42484-023-00119-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42484-023-00119-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,24]],"date-time":"2024-10-24T08:36:44Z","timestamp":1729759004000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s42484-023-00119-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,17]]},"references-count":56,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,12]]}},"alternative-id":["119"],"URL":"https:\/\/doi.org\/10.1007\/s42484-023-00119-y","relation":{},"ISSN":["2524-4906","2524-4914"],"issn-type":[{"value":"2524-4906","type":"print"},{"value":"2524-4914","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,17]]},"assertion":[{"value":"12 December 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 June 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 July 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Human and animal ethics"}},{"value":"This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article\u2019s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article\u2019s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"The authors declare no competing interests.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"28"}}