{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T16:58:23Z","timestamp":1765040303034},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2010,11,8]],"date-time":"2010-11-08T00:00:00Z","timestamp":1289174400000},"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":[[2010,12]]},"abstract":"<jats:p>The spatial search problem consists of minimising the number of steps required to find a given site in a network under the restriction that only oracle queries or translations to neighbouring sites are allowed. We propose a quantum algorithm for the spatial search problem on a honeycomb lattice with<jats:italic>N<\/jats:italic>sites and torus-like boundary conditions. The search algorithm is based on a modified quantum walk on an hexagonal lattice and the general framework proposed by Ambainis, Kempe and Rivosh (Ambainis<jats:italic>et al<\/jats:italic>. 2005) is employed to show that the time complexity of this quantum search algorithm is<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0960129510000332_inline1\"><jats:alt-text>$O(\\sqrt{N \\log N})$<\/jats:alt-text><\/jats:inline-graphic>.<\/jats:p>","DOI":"10.1017\/s0960129510000332","type":"journal-article","created":{"date-parts":[[2010,11,8]],"date-time":"2010-11-08T11:00:45Z","timestamp":1289214045000},"page":"999-1009","source":"Crossref","is-referenced-by-count":37,"title":["Spatial search on a honeycomb network"],"prefix":"10.1017","volume":"20","author":[{"given":"G.","family":"ABAL","sequence":"first","affiliation":[]},{"given":"R.","family":"DONANGELO","sequence":"additional","affiliation":[]},{"given":"F. L.","family":"MARQUEZINO","sequence":"additional","affiliation":[]},{"given":"R.","family":"PORTUGAL","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2010,11,8]]},"reference":[{"key":"S0960129510000332_ref2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.48.1687"},{"key":"S0960129510000332_ref8","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.70.022314"},{"key":"S0960129510000332_ref16","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.71.622"},{"key":"S0960129510000332_ref14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.78.012310"},{"key":"S0960129510000332_ref13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.67.052307"},{"key":"S0960129510000332_ref15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.97.150504"},{"key":"S0960129510000332_ref3","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2004.54"},{"key":"S0960129510000332_ref12","volume-title":"Introduction to Solid State Physics","author":"Kittel","year":"1995"},{"key":"S0960129510000332_ref10","doi-asserted-by":"crossref","unstructured":"Geim A. K. and MacDonald A. H. (2007) Graphene: exploring carbon flatland Phys. Today 35\u201341.","DOI":"10.1063\/1.2774096"},{"key":"S0960129510000332_ref1","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.2003.1238194"},{"key":"S0960129510000332_ref6","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539796300933"},{"key":"S0960129510000332_ref9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.58.915"},{"key":"S0960129510000332_ref4","unstructured":"Ambainis A. , Kempe J. and Rivosh A. (2005) Coins make quantum walks faster. In: SODA '05: Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms 1099\u20131108."},{"key":"S0960129510000332_ref7","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/305\/05215"},{"key":"S0960129510000332_ref5","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/305\/05212"},{"key":"S0960129510000332_ref11","first-page":"212","volume-title":"Proc. 28th Annual ACM Symposium on the Theory of Computation","author":"Grover","year":"1996"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129510000332","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,1]],"date-time":"2024-04-01T01:28:02Z","timestamp":1711934882000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129510000332\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,11,8]]},"references-count":16,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2010,12]]}},"alternative-id":["S0960129510000332"],"URL":"https:\/\/doi.org\/10.1017\/s0960129510000332","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,11,8]]}}}