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• W2895574305 abstract "In this paper we present an efficiently scaling quantum algorithm which finds the size of the maximum common edge subgraph for a pair of arbitrary graphs and thus provides a meaningful measure of graph similarity. The algorithm makes use of a two-part quantum dynamic process: in the first part we obtain information crucial for the comparison of two graphs through linear quantum computation. However, this information is hidden in the quantum system with vanishingly small amplitude that even quantum algorithms such as Grover's search are not fast enough to distill the information efficiently. In order to extract the information we call upon techniques in nonlinear quantum computing to provide the speed-up necessary for an efficient algorithm. The linear quantum circuit requires $mathcal{O}(n^3 log^3 (n) log log (n))$ elementary quantum gates and the nonlinear evolution under the Gross-Pitaevskii equation has a time scaling of $mathcal{O}(frac{1}{g} n^2 log^3 (n) log log (n))$, where $n$ is the number of vertices in each graph and $g$ is the strength of the Gross-Pitaveskii non-linearity. Through this example, we demonstrate the power of nonlinear quantum search techniques to solve a subset of NP-hard problems." @default.
• W2895574305 created "2018-10-12" @default.
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• W2895574305 date "2018-10-03" @default.
• W2895574305 modified "2023-09-27" @default.
• W2895574305 title "Graph comparison via nonlinear quantum search" @default.
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• W2895574305 doi "https://doi.org/10.48550/arxiv.1810.01647" @default.
• W2895574305 hasPublicationYear "2018" @default.
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