科研之友
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摘要
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 N-1/4. This is a significant, but not unreasonable, improvement over the N-1/2 scaling of Grover's algorithm. Since the Gross-Pitaevskii equation approximates the multi-particle (linear) Schrodinger 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.
- 出版日期2013-6-12
