Nonlinear quantum search using the Gross–Pitaevskii equation

Por • 27 jun, 2013 • Sección: Leyes

David A Meyer1 and Thomas G Wong2

Paper. 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

New Journal of Physics Volume 15 June 2013

David A Meyer and Thomas G Wong 2013 New J. Phys. 15 063014 doi:10.1088/1367-2630/15/6/063014

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