Controlled quantum search

  • K. de Lacy
  • L. Noakes
  • J. Twamley
  • J. B. Wang


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, 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.


Control system Nonlinear quantum search Gross–Pitaevskii 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of Western AustraliaPerthAustralia
  2. 2.Department of Physics and Astronomy, ARC Centre for Engineered Quantum SystemsMacquarie UniversitySydneyAustralia
  3. 3.School of Physics and AstrophysicsUniversity of Western AustraliaPerthAustralia

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