Skip to main content
×
Home
    • Aa
    • Aa

Spatial quantum search in a triangular network

  • G. ABAL (a1), R. DONANGELO (a1), M. FORETS (a1) and R. PORTUGAL (a2)
Abstract

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 N 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 et al. (2005) and Tulsi in Tulsi (2008) applied to a triangular network. The AKR–Tulsi formalism was employed to show that the time complexity of the quantum search on the triangular lattice is .

Copyright
References
Hide All
Abal G., Donangelo R., Marquezino F. and Portugal R. (2010) Spatial search in a honeycomb network. Mathematical Structures in Computer Science 20 (6)9991009.
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) 200–209.
Ambainis A., Kempe J. and Rivosh A. (2005) Coins make quantum walks faster. SODA '05: Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms 78 (2)10991108.
Benioff P. (2002) Space searches with a quantum robot. In: Lomonaco S. J. and Brandt H. E. (eds.) Quantum Computation and Information, Contemporary Mathematics Series, AMS.
Grover L. (1996) A fast quantum mechanical algorithm for database search. Proceedings 28th Annual ACM Symposium on the Theory of Computation, ACM Press 212219.
Grover L. (1997) Quantum mechanics helps in searching for a needle in a haystack. Physical Review Letters 78 (2)325328.
Kittel C. (1995) Introduction to Solid State Physics, 7th edition, Wiley.
Krovi H., Magniez F., Ozols M. and Roland J. (2010) Finding is as easy as detecting for quantum walks. In: Abramsky S., Gavoille C., Kirchner C., auf der Heide F. M. and Spirakis P. G. (eds.) Proceedings of the 37th international colloquium conference on Automata, languages and programming (ICALP'10). Springer-Verlag Lecture Notes in Computer Science 6198 540551.
Magniez F., Nayak A., Richter P. and Santha M. (2009) On the hitting times of quantum versus random walks. Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '09) 86–95.
Shenvi N., Kempe J. and Birgitta Whaley, F. (2003) A quantum random walk search algorithm. Physical Review A 67 052307.
Tulsi A. (2008) Faster quantum walk algorithm for the two dimensional spatial search. Physical Review A 78 (1) 012310-1–012310-6.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 3 *
Loading metrics...

Abstract views

Total abstract views: 68 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 20th October 2017. This data will be updated every 24 hours.