{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T16:59:22Z","timestamp":1765040362322},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2012,2,9]],"date-time":"2012-02-09T00:00:00Z","timestamp":1328745600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2012,6]]},"abstract":"<jats:p>The spatial search problem consists of minimising the number of steps required to find a given site in a network, with the restriction that only an oracle query or a translation to a neighbouring site is allowed at each step. We propose a quantum algorithm for the spatial search problem on a triangular lattice with <jats:italic>N<\/jats:italic> sites and torus-like boundary conditions. The proposed algorithm is a special case of the general framework for abstract search proposed by Ambainis, Kempe and Rivosh (AKR) in Ambainis <jats:italic>et al<\/jats:italic>. (2005) and Tulsi in Tulsi (2008) applied to a triangular network. The AKR\u2013Tulsi formalism was employed to show that the time complexity of the quantum search on the triangular lattice is <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0960129511000600_inline1\"><jats:alt-text>$O(\\sqrt{N \\log N})$<\/jats:alt-text><\/jats:inline-graphic>.<\/jats:p>","DOI":"10.1017\/s0960129511000600","type":"journal-article","created":{"date-parts":[[2012,2,9]],"date-time":"2012-02-09T07:15:09Z","timestamp":1328771709000},"page":"521-531","source":"Crossref","is-referenced-by-count":14,"title":["Spatial quantum search in a triangular network"],"prefix":"10.1017","volume":"22","author":[{"given":"G.","family":"ABAL","sequence":"first","affiliation":[]},{"given":"R.","family":"DONANGELO","sequence":"additional","affiliation":[]},{"given":"M.","family":"FORETS","sequence":"additional","affiliation":[]},{"given":"R.","family":"PORTUGAL","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2012,2,9]]},"reference":[{"key":"S0960129511000600_ref4","volume-title":"Quantum Computation and Information","author":"Benioff","year":"2002"},{"key":"S0960129511000600_ref2","unstructured":"Ambainis A. and Aaronson S. (2003) Quantum search of spatial regions. In: Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science (FOCS) 200\u2013209."},{"key":"S0960129511000600_ref6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.79.325"},{"key":"S0960129511000600_ref9","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611973068.10"},{"key":"S0960129511000600_ref3","first-page":"1099","article-title":"Coins make quantum walks faster","volume":"78","author":"Ambainis","year":"2005","journal-title":"SODA '05: Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms"},{"key":"S0960129511000600_ref1","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129510000332"},{"key":"S0960129511000600_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-14165-2_46"},{"key":"S0960129511000600_ref5","first-page":"212","volume-title":"Proceedings 28th Annual ACM Symposium on the Theory of Computation","author":"Grover","year":"1996"},{"key":"S0960129511000600_ref7","volume-title":"Introduction to Solid State Physics","author":"Kittel","year":"1995"},{"key":"S0960129511000600_ref10","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.67.052307"},{"key":"S0960129511000600_ref11","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.78.012310"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129511000600","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,25]],"date-time":"2019-04-25T17:03:44Z","timestamp":1556211824000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129511000600\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2,9]]},"references-count":11,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2012,6]]}},"alternative-id":["S0960129511000600"],"URL":"https:\/\/doi.org\/10.1017\/s0960129511000600","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,2,9]]}}}