Quantum search with general nonlinearities

David A. Meyer, Thomas G. Wong

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


Evolution by the Gross-Pitaevskii equation, which describes Bose-Einstein condensates under certain conditions, solves the unstructured search problem more efficiently than does the Schrödinger equation, because it includes a cubic nonlinearity, proportional to |ψ|2ψ. This is not the only nonlinearity of the form f(|ψ|2)ψ that arises in effective equations for the evolution of real quantum physical systems, however: The cubic-quintic nonlinear Schrödinger equation describes light propagation in nonlinear Kerr media with defocusing corrections, and the logarithmic nonlinear Schrödinger equation describes Bose liquids under certain conditions. Analysis of computation with such systems yields some surprising results; for example, when time-measurement precision is included in the resource accounting, searching a "database" when there is a single correct answer may be easier than searching when there are multiple correct answers. In each of these cases the nonlinear equation is an effective approximation to a multiparticle Schrödinger equation, for search by which Grover's algorithm is optimal. Thus our results lead to quantum information-theoretic bounds on the physical resources required for these effective nonlinear theories to hold, asymptotically.

Original languageEnglish (US)
Article number012312
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number1
StatePublished - Jan 14 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics


Dive into the research topics of 'Quantum search with general nonlinearities'. Together they form a unique fingerprint.

Cite this