{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,3]],"date-time":"2025-09-03T09:53:16Z","timestamp":1756893196498,"version":"3.37.3"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"12","license":[{"start":{"date-parts":[[2019,10,22]],"date-time":"2019-10-22T00:00:00Z","timestamp":1571702400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,10,22]],"date-time":"2019-10-22T00:00:00Z","timestamp":1571702400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"the Science and Technology Program of Shenzhen of China","award":["JCYJ20180306124612893"],"award-info":[{"award-number":["JCYJ20180306124612893"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2019,12]]},"DOI":"10.1007\/s11128-019-2475-3","type":"journal-article","created":{"date-parts":[[2019,10,23]],"date-time":"2019-10-23T04:26:01Z","timestamp":1571804761000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["One-dimensional quantum walks with two-step memory"],"prefix":"10.1007","volume":"18","author":[{"given":"Qing","family":"Zhou","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4489-2488","authenticated-orcid":false,"given":"Songfeng","family":"Lu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,10,22]]},"reference":[{"key":"2475_CR1","first-page":"37","volume-title":"STOC, Hersonissos, Greece 2001","author":"A Ambainis","year":"2001","unstructured":"Ambainis, A., Bach, E., Nayak, A., Vishwanath, A., Watrous, J.: One-dimensional quantum walks. In: Vitter, J.S., Spirakis, P., Mihalis, Y. (eds.) STOC, Hersonissos, Greece 2001, pp. 37\u201349. ACM, New York (2001)"},{"issue":"2","key":"2475_CR2","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1007\/s11128-018-2158-5","volume":"18","author":"X Xue","year":"2019","unstructured":"Xue, X., Ruan, Y., Liu, Z.: Discrete-time quantum walk search on Johnson graphs. Quantum Inf. Process. 18(2), 50 (2019)","journal-title":"Quantum Inf. Process."},{"issue":"5","key":"2475_CR3","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1007\/s11128-019-2270-1","volume":"18","author":"Y Feng","year":"2019","unstructured":"Feng, Y., Shi, R., Shi, J., Zhou, J., Guo, Y.: Arbitrated quantum signature scheme with quantum walk-based teleportation. Quantum Inf. Process. 18(5), 154 (2019)","journal-title":"Quantum Inf. Process."},{"issue":"3","key":"2475_CR4","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1007\/s11128-019-2171-3","volume":"18","author":"S Marsh","year":"2019","unstructured":"Marsh, S., Wang, J.B.: A quantum walk-assisted approximate algorithm for bounded NP optimisation problems. Quantum Inf. Process. 18(3), 61 (2019)","journal-title":"Quantum Inf. Process."},{"issue":"11","key":"2475_CR5","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1007\/s11128-018-2055-y","volume":"17","author":"C Vlachou","year":"2018","unstructured":"Vlachou, C., Krawec, W., Mateus, P., Paunkovi\u0107, N., Souto, A.: Quantum key distribution with quantum walks. Quantum Inf. Process. 17(11), 288 (2018)","journal-title":"Quantum Inf. Process."},{"issue":"6","key":"2475_CR6","doi-asserted-by":"publisher","first-page":"1861","DOI":"10.1007\/s10773-019-04081-z","volume":"58","author":"Y Yang","year":"2019","unstructured":"Yang, Y., Bi, J., Li, D., Zhou, Y., Shi, W.: Hash function based on quantum walks. Int. J. Theor. Phys. 58(6), 1861\u20131873 (2019)","journal-title":"Int. J. Theor. Phys."},{"issue":"5","key":"2475_CR7","first-page":"509","volume":"10","author":"MM Gettrick","year":"2010","unstructured":"Gettrick, M.M.: One dimensional quantum walks with memory. Quantum Inf. Comput. 10(5), 509\u2013524 (2010)","journal-title":"Quantum Inf. Comput."},{"issue":"11","key":"2475_CR8","first-page":"1004","volume":"10","author":"N Konno","year":"2010","unstructured":"Konno, N., Machida, T.: Limit theorems for quantum walks with memory. Quantum Inf. Comput. 10(11), 1004\u20131017 (2010)","journal-title":"Quantum Inf. Comput."},{"issue":"03","key":"2475_CR9","doi-asserted-by":"publisher","first-page":"1850014","DOI":"10.1142\/S1230161218500142","volume":"25","author":"NP Kumar","year":"2018","unstructured":"Kumar, N.P., Banerjee, S., Srikanth, R., Jagadish, V., Petruccione, F.: Non-Markovian evolution: a quantum walk perspective. Open Syst. Inf. Dyn. 25(03), 1850014 (2018)","journal-title":"Open Syst. Inf. Dyn."},{"issue":"9","key":"2475_CR10","doi-asserted-by":"publisher","first-page":"094001","DOI":"10.1088\/0034-4885\/77\/9\/094001","volume":"77","author":"A Rivas","year":"2014","unstructured":"Rivas, A., Huelga, S.F., Plenio, M.B.: Quantum non-Markovianity: characterization, quantification and detection. Rep. Prog. Phys. 77(9), 094001 (2014)","journal-title":"Rep. Prog. Phys."},{"issue":"5","key":"2475_CR11","doi-asserted-by":"publisher","first-page":"052330","DOI":"10.1103\/PhysRevA.89.052330","volume":"89","author":"M Hinarejos","year":"2014","unstructured":"Hinarejos, M., Franco, C.D., Romanelli, A., P\u00e9rez, A.: Chirality asymptotic behavior and non-Markovianity in quantum walks on a line. Phys. Rev. A 89(5), 052330 (2014)","journal-title":"Phys. Rev. A"},{"key":"2475_CR12","doi-asserted-by":"crossref","unstructured":"Zhou, Q., Lu, S.: One dimensional quantum walks with two-step memory. \narXiv:1904.06528\n\n (2019). Accessed 2019","DOI":"10.1007\/s11128-019-2475-3"},{"key":"2475_CR13","first-page":"A23","volume":"4","author":"D Merlini","year":"2004","unstructured":"Merlini, D., Uncini, F., Verri, M.C.: A unified approach to the study of general and palindromic compositions. Integers Electron. J. Comb. Number Theory 4, A23 (2004)","journal-title":"Integers Electron. J. Comb. Number Theory"},{"key":"2475_CR14","unstructured":"Brualdi, R.A.: Permutations and combinations. In: Zhenchun, C. (ed.) Introductory Combinatorics, pp. 32\u201333. China Machine Press, Beijing (2009)"},{"issue":"30","key":"2475_CR15","doi-asserted-by":"publisher","first-page":"7581","DOI":"10.1088\/0305-4470\/37\/30\/013","volume":"37","author":"AP Flitney","year":"2003","unstructured":"Flitney, A.P., Abbott, D.: Quantum walks with history dependence. J. Phys. A Math. Gen. 37(30), 7581 (2003)","journal-title":"J. Phys. A Math. Gen."},{"key":"2475_CR16","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1016\/j.physa.2014.01.002","volume":"399","author":"MM Gettrick","year":"2014","unstructured":"Gettrick, M.M., Miszczak, J.A.: Quantum walks with memory on cycles. Phys. A Stat. Mech. Appl. 399, 163 (2014)","journal-title":"Phys. A Stat. Mech. Appl."},{"issue":"4","key":"2475_CR17","doi-asserted-by":"publisher","first-page":"042323","DOI":"10.1103\/PhysRevA.93.042323","volume":"93","author":"D Li","year":"2016","unstructured":"Li, D., Gettrick, M.M., Gao, F., Xu, J., Wen, Q.Y.: Generic quantum walks with memory on regular graphs. Phys. Rev. A 93(4), 042323 (2016)","journal-title":"Phys. Rev. A"},{"issue":"5","key":"2475_CR18","doi-asserted-by":"publisher","first-page":"052302","DOI":"10.1103\/PhysRevA.87.052302","volume":"87","author":"PP Rohde","year":"2013","unstructured":"Rohde, P.P., Brennen, G.K., Gilchrist, A.: Quantum walks with memory provided by recycled coins and a memory of the coin-flip history. Phys. Rev. A 87(5), 052302 (2013)","journal-title":"Phys. Rev. A"},{"issue":"17","key":"2475_CR19","doi-asserted-by":"publisher","first-page":"175304","DOI":"10.1088\/1751-8113\/42\/17\/175304","volume":"42","author":"JB Stang","year":"2009","unstructured":"Stang, J.B., Rezakhani, A.T., Sanders, B.C.: Correlation effects in a discrete quantum random walk. J. Phys. A Math. Theor. 42(17), 175304 (2009)","journal-title":"J. Phys. A Math. Theor."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-019-2475-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11128-019-2475-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-019-2475-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,20]],"date-time":"2020-10-20T23:23:43Z","timestamp":1603236223000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11128-019-2475-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,22]]},"references-count":19,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["2475"],"URL":"https:\/\/doi.org\/10.1007\/s11128-019-2475-3","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"type":"print","value":"1570-0755"},{"type":"electronic","value":"1573-1332"}],"subject":[],"published":{"date-parts":[[2019,10,22]]},"assertion":[{"value":"9 May 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 October 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 October 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"359"}}