2013/03/31 by David A. Meyer, Thomas G. Wong · 1 citation
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1088/1367-2630/15/6/063014
published as New J. Phys. 15 (2013) 063014 · 15 pages, 6 figures
arxiv created 2013/06/13 · arxiv updated 2013/06/14
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.