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 …

In this survey paper we give an intuitive treatment of the discrete time quantization of
classical Markov chains. Grover search and the quantum walk based search algorithms of …

Quantum mechanical computers can solve certain problems asymptotically faster than any
classical computing device. Several fast quantum algorithms are known, but the nature of …

We propose a new method for designing quantum search algorithms forfinding a" marked"
element in the state space of a classical Markovchain. The algorithm is based on a quantum …

This tutorial article showcases the many varieties and uses of quantum walks. Discrete time
quantum walks are introduced as counterparts of classical random walks. The emphasis is …

Motivated by the immense success of random walk and Markov chain methods in the design
of classical algorithms, we consider_quantum_ walks on graphs. We analyse in detail the …

A quantum walk algorithm can detect the presence of a marked vertex on a graph
quadratically faster than the corresponding random walk algorithm (Szegedy, FOCS 2004) …

QUANTUM WALKS AND THEIR ALGORITHMIC APPLICATIONS | International Journal of
Quantum Information World Scientific Search This Journal Anywhere Quick Search in Journals …

Quantum random walks on graphs have been shown to display many interesting properties,
including exponentially fast hitting times when compared with their classical counterparts …

The hitting time of a classical random walk (Markov chain) is the time required to detect the
presence of—or equivalently, to find—a marked state. The hitting time of a quantum walk is …