{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T18:17:28Z","timestamp":1768414648473,"version":"3.49.0"},"reference-count":20,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2022,8,29]],"date-time":"2022-08-29T00:00:00Z","timestamp":1661731200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FCT, Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","award":["UIDB\/50021\/2020"],"award-info":[{"award-number":["UIDB\/50021\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>We indicate the quantum tree search qiskit implementation by popular examples from symbolical artificial intelligence, the 3-puzzle, 8-puzzle and the ABC blocks world. Qiskit is an open-source software development kit (SDK) for working with quantum computers at the level of circuits and algorithms from IBM. The objects are represented by symbols and adjectives. Two principles are presented. Either the position description (adjective) is fixed and the class descriptors moves (is changed) or, in the reverse interpretation, the class descriptor is fixed and the position descriptor (adjective) moves (is changed). We indicate how to decompose the permutation operator that executes the rules by the two principles. We demonstrate that the the branching factor is reduced by Grover\u2019s amplification to the square root of the average branching factor and not to the maximal branching factor as previously assumed.<\/jats:p>","DOI":"10.3390\/math10173103","type":"journal-article","created":{"date-parts":[[2022,8,29]],"date-time":"2022-08-29T22:53:42Z","timestamp":1661813622000},"page":"3103","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Quantum Tree Search with Qiskit"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2179-4378","authenticated-orcid":false,"given":"Andreas","family":"Wichert","sequence":"first","affiliation":[{"name":"Department of Computer Science and Engineering, INESC-ID & Instituto Superior T\u00e9cnico, University of Lisbon, 2740-122 Porto Salvo, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Nilsson, N.J. (1982). Principles of Artificial Intelligence, Springer.","DOI":"10.1007\/978-3-662-09438-9"},{"key":"ref_2","unstructured":"Anderson, J.R. (1995). Cognitive Psychology and Its Implications, W. H. Freeman and Company. [4th ed.]."},{"key":"ref_3","unstructured":"Brownston, L., Farell, R., Kant, E., and Martin, N. (1985). Programming Expert Systems in OPS5: An Introduction to Rule-Based Programming, Addison-Wesley."},{"key":"ref_4","unstructured":"Luger, G.F., and Stubblefield, W.A. (1998). Artificial Intelligence, Structures and Strategies for Complex Problem Solving, Addison-Wesley. [3rd ed.]."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Wichert, A. (2020). Principles of Quantum Artificial Intelligence: Quantum Problem Solving and Machine Learning, World Scientific. [2nd ed.].","DOI":"10.1142\/11938"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1007\/s11128-010-0212-z","article-title":"Tree search and quantum computation","volume":"10","author":"Tarrataca","year":"2011","journal-title":"Quantum Inf. Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/0004-3702(85)90084-0","article-title":"Depth-first iterative-deepening: An optimal admissible tree search","volume":"27","author":"Korf","year":"1985","journal-title":"Artif. Intell."},{"key":"ref_8","unstructured":"Russell, S., and Norvig, P. (2010). Artificial Intelligence: A Modern Approach, Prentice Hall."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Tarrataca, L., and Wichert, A. (2013). Quantum iterative deepening with an application to the halting problem. PLoS ONE, 8.","DOI":"10.1371\/journal.pone.0057309"},{"key":"ref_10","unstructured":"Eagle, A., Kato, T., and Minato, Y. (2019). Solving tiling puzzles with quantum annealing. arXiv."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Hamze, F., Jacob, D.C., Ochoa, A.J., Perera, D., Wang, W., and Katzgrabe, H.G. (2018). From near to eternity: Spin-glass planting, tiling puzzles, and constraint satisfaction problems. arXiv.","DOI":"10.1103\/PhysRevE.97.043303"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Takabatake, K., Yanagisawa, K., and Akiyama, Y. (2022). Solving generalized polyomino puzzles using the ising model. Entropy, 24.","DOI":"10.3390\/e24030354"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1126\/science.284.5415.779","article-title":"Quantum annealing of a disordered magnet","volume":"284","author":"Brooke","year":"1999","journal-title":"Science"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1038\/nature10012","article-title":"Quantum annealing with manufactured spins","volume":"473","author":"Johnson","year":"2011","journal-title":"Nature"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"McGeoch, C.C. (2014). Adiabatic Quantum Computation and Quantum Annealing: Theory and Practice, Morgan & Claypool.","DOI":"10.1007\/978-3-031-02518-1"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Hertz, J., Krogh, A., and Palmer, R.G. (1991). Introduction to the Theory of Neural Computation, Addison-Wesley.","DOI":"10.1063\/1.2810360"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1007\/s12559-011-9103-6","article-title":"Problem-solving and quantum computation","volume":"3","author":"Tarrataca","year":"2011","journal-title":"Cogn. Comput."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1137\/07070111X","article-title":"Tensor decompositions and applications","volume":"51","author":"Kolda","year":"2009","journal-title":"SIAM Rev."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Hirvensalo, M. (2004). Quantum Computing, Springer.","DOI":"10.1007\/978-3-662-09636-9"},{"key":"ref_20","unstructured":"Nielsen, M.A., and Chuang, I.L. (2000). Quantum Computation and Quantum Information, Cambridge University Press."}],"container-title":["Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2227-7390\/10\/17\/3103\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:19:40Z","timestamp":1760141980000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2227-7390\/10\/17\/3103"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,29]]},"references-count":20,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["math10173103"],"URL":"https:\/\/doi.org\/10.3390\/math10173103","relation":{},"ISSN":["2227-7390"],"issn-type":[{"value":"2227-7390","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,29]]}}}