Quantum Complexity of Testing Group Commutativity

@article{Magniez2007QuantumCO,
  title={Quantum Complexity of Testing Group Commutativity},
  author={Fr{\'e}d{\'e}ric Magniez and Ashwin Nayak},
  journal={Algorithmica},
  year={2007},
  volume={48},
  pages={221-232}
}
AbstractWe consider the problem of testing the commutativity of a black-box group specified by its k generators. The complexity (in terms of k) of this problem was first considered by Pak, who gave a randomized algorithm involving O(k) group operations. We construct a quite optimal quantum algorithm for this problem whose complexity is in $\tilde{O}(k^{2/3})$. The algorithm uses and highlights the power of the quantization method of Szegedy. For the lower bound of $\Omega(k^{2/3})$, we give a… Expand
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