Quantum speed-up of Markov chain based algorithms

@article{Szegedy2004QuantumSO,
  title={Quantum speed-up of Markov chain based algorithms},
  author={Mario Szegedy},
  journal={45th Annual IEEE Symposium on Foundations of Computer Science},
  year={2004},
  pages={32-41}
}
  • M. Szegedy
  • Published 17 October 2004
  • Computer Science
  • 45th Annual IEEE Symposium on Foundations of Computer Science
We develop a generic method for quantizing classical algorithms based on random walks. We show that under certain conditions, the quantum version gives rise to a quadratic speed-up. This is the case, in particular, when the Markov chain is ergodic and its transition matrix is symmetric. This generalizes the celebrated result of L. K. Grover (1996)and a number of more recent results, including the element distinctness result of Ambainis and the result of Ambainis, Kempe and Rivosh that computes… 
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