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Quantum Information Processing

Controlled quantum search

  • 01-10-2018
Published in:
Authors
K. de Lacy
L. Noakes
J. Twamley
J. B. Wang
Published in
Quantum Information Processing | Issue 10/2018

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Abstract

Quantum searching for one of N marked items in an unsorted database of n items is solved in \(\mathcal {O}(\sqrt{n/N})\) steps using Grover’s algorithm. Using nonlinear quantum dynamics with a Gross–Pitaevskii-type quadratic nonlinearity, Childs and Young (Phys Rev A 93:022314, 2016, https://doi.org/10.1103/PhysRevA.93.022314) discovered an unstructured quantum search algorithm with a complexity \(\mathcal {O}( \min \{ 1/g \, \log (g n), \sqrt{n} \}) \), which can be used to find a marked item after \(o(\log (n))\) repetitions, where g is the nonlinearity strength. In this work we develop an quantum search on a complete graph using a time-dependent nonlinearity which obtains one of the N marked items with certainty. The protocol has runtime \(\mathcal {O}(n /(g \sqrt{N(n-N)}))\), where g is related to the time-dependent nonlinearity. We also extend the analysis to a quantum search on general symmetric graphs and can greatly simplify the resulting equations when the graph diameter is less than 4.

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previous article Absorption probabilities of quantum walks
next article Two families of BCH codes and new quantum codes
Title
Controlled quantum search
Authors
K. de Lacy
L. Noakes
J. Twamley
J. B. Wang
Publication date
01-10-2018
Publisher
Springer US
Published in
Quantum Information Processing / Issue 10/2018
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-018-2031-6
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