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Quantum Studies: Mathematics and Foundations

, Volume 5, Issue 4, pp 551–577 | Cite as

Quantum search on simplicial complexes

  • Kaname MatsueEmail author
  • Osamu Ogurisu
  • Etsuo Segawa
Regular Paper

Abstract

In this paper, we propose an extension of quantum searches on graphs driven by quantum walks to simplicial complexes. To this end, we define a new quantum walk on simplicial complex which is an alternative of preceding studies by authors. We show that the quantum search on the specific simplicial complex corresponding to the triangulation of n-dimensional unit square driven by this new simplicial quantum walk works well, namely, a marked simplex can be found with probability \(1+o(1)\) within a time \(O(\sqrt{N})\), where N is the number of simplices with the dimension of marked simplex.

Keywords

Quantum walks Quantum search Simplicial complexes Unitary equivalence of quantum walks 

Notes

Acknowledgements

KM was partially supported by Program for Promoting the reform of national universities (Kyushu University), Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan, World Premier International Research Center Initiative (WPI), MEXT, Japan, and JSPS Grant-in-Aid for Young Scientists (B) (No. JP17K14235). OO was partially supported by JSPS KAKENHI Grant (Nos. JP24540208, JP16K05227). ES acknowledges financial support from the Grant-in-Aid for Young Scientists (B) and of Scientific Research (B) Japan Society for the Promotion of Science (Grant No. JP16K17637, No. JP16K03939). Finally, authors would thank to reviewers for providing them helpful comments about contents of the paper.

Supplementary material

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Copyright information

© Chapman University 2017

Authors and Affiliations

  1. 1.Institute of Mathematics for Industry/International Institute for Carbon-Neutral Energy Research (WPI-I²CNER)Kyushu UniversityFukuokaJapan
  2. 2.Division of Mathematical and Physical SciencesKanazawa UniversityKanazawaJapan
  3. 3.Graduate School of Information SciencesTohoku UniversityAobaJapan

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