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arXiv · 1601.01154

Continuous-Time Quantum Search on Balanced Trees

Pascal Philipp·Luís Tarrataca·Stefan Boettcher
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Abstract

We examine the effect of network heterogeneity on the performance of quantum search algorithms. To this end, we study quantum search on a tree for the oracle Hamiltonian formulation employed by continuous-time quantum walks. We use analytical and numerical arguments to show that the exponent of the asymptotic running time $\sim N^{\beta}$ changes uniformly from $\beta=0.5$ to $\beta=1$ as the searched-for site is moved from the root of the tree towards the leaves. These results imply that the time complexity of the quantum search algorithm on a balanced tree is closely correlated with certain path-based centrality measures of the searched-for site.

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Pascal Philipp, Luís Tarrataca, Stefan Boettcher. 2016-01-06. Continuous-Time Quantum Search on Balanced Trees. https://doi.org/10.1103/physreva.93.032305

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