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Spatial quantum search in a triangular network†

Published online by Cambridge University Press:  09 February 2012

G. ABAL ,
R. DONANGELO ,
M. FORETS  and
R. PORTUGAL
G. ABAL
Affiliation:
Instituto de Física, Facultad de Ingeniería, UdelaR, C.C. 30, C.P. 11300, Montevideo, Uruguay Email: abal@fing.edu.uy, donangel@fing.edu.uy, mforets@fing.edu.uy
R. DONANGELO
Affiliation:
Instituto de Física, Facultad de Ingeniería, UdelaR, C.C. 30, C.P. 11300, Montevideo, Uruguay Email: abal@fing.edu.uy, donangel@fing.edu.uy, mforets@fing.edu.uy
M. FORETS
Affiliation:
Instituto de Física, Facultad de Ingeniería, UdelaR, C.C. 30, C.P. 11300, Montevideo, Uruguay Email: abal@fing.edu.uy, donangel@fing.edu.uy, mforets@fing.edu.uy
R. PORTUGAL
Affiliation:
Laboratório Nacional de Computação Científica - LNCC, Av. Getúlio Vargas 333, Petrópolis, RJ, 25651-075, Brazil Email: portugal@lncc.br
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Abstract

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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 $O(\sqrt{N \log N})$.

Information

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 22 , Issue 3 , June 2012 , pp. 521 - 531
Copyright
Copyright © Cambridge University Press 2012

References

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