期刊
QUANTUM INFORMATION PROCESSING
卷 17, 期 10, 页码 -出版社
SPRINGER
DOI: 10.1007/s11128-018-2031-6
关键词
Control system; Nonlinear quantum search; Gross-Pitaevskii
Quantum searching for one of N marked items in an unsorted database of n items is solved in steps using Grover's algorithm. Using nonlinear quantum dynamics with a Gross-Pitaevskii-type quadratic nonlinearity, Childs and Young (Phys Rev A 93:022314, 2016, discovered an unstructured quantum search algorithm with a complexity , which can be used to find a marked item after repetitions, where g is the nonlinearity strength. In this work we develop an quantum search on a complete graph using a time-dependent nonlinearity which obtains one of the N marked items with certainty. The protocol has runtime , where g is related to the time-dependent nonlinearity. We also extend the analysis to a quantum search on general symmetric graphs and can greatly simplify the resulting equations when the graph diameter is less than 4.
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