# 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} }

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…

## 532 Citations

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