1205.1534 (Aleksandrs Belovs)

Learning-graph-based Quantum Algorithm for k-distnictness    [PDF]

Aleksandrs Belovs

In this paper, we present a quantum algorithm solving the $k$-distinctness problem in $O(n^{1-2^{k-2}/(2^k-1)})$ queries with a bounded error. This improves the previous $O(n^{k/(k+1)})$-query algorithm by Ambainis. The construction uses a modified learning graph approach. Compared to the recent paper by Belovs and Lee arXiv:1108.3022, the algorithm doesn't require any prior information on the input, and the complexity analysis is much simpler. Additionally, we introduce an $O(\sqrt{n}\alpha^{1/6})$ algorithm for the graph collision problem where $\alpha=\alpha(G)$ is the independence number of the graph.

View original: http://arxiv.org/abs/1205.1534