Nonlinear quantum search using the Gross-Pitaevskii equation

David A. Meyer, Thomas Wong

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Abstract

We solve the unstructured search problem in constant time by computing with a physically motivated nonlinearity of the Gross-Pitaevskii type. This speedup comes, however, at the novel expense of increasing the time-measurement precision. Jointly optimizing these resource requirements results in an overall scaling of N1/4. This is a significant, but not unreasonable, improvement over the N1/2 scaling of Grover's algorithm. Since the Gross-Pitaevskii equation approximates the multi-particle (linear) Schrödinger equation, for which Grover's algorithm is optimal, our result leads to a quantum information-theoretic lower bound on the number of particles needed for this approximation to hold, asymptotically.

Original languageEnglish (US)
Article number063014
JournalNew Journal of Physics
Volume15
DOIs
StatePublished - Jun 1 2013
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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