We consider 1-way quantum finite automata (QFAs). First, we compare them with their classical counterparts. We show that, if an automaton is required to give the correct answer with a largeâ€¦ (More)

We introduce 2-way finite automata with quantum and classical states (2qcfa's). This is a variant on the 2-way quantum finite automata (2qfa) model which may be simpler to implement than unrestrictedâ€¦ (More)

We set the ground for a theory of quantum walks on graphs-the generalization of random walks on finite graphs to the quantum world. Such quantum walks do not converge to any stationary distribution,â€¦ (More)

We show how to search <i>N</i> items arranged on a âˆš<i>N</i> Ã— âˆš<i>N</i> grid in time <i>O</i>(âˆš<i>N</i> log <i>N</i>), using a discrete time quantum walk. This result for the first time exhibits aâ€¦ (More)

We define and analyze quantum computational variants of random walks on one-dimensional lattices. In particular, we analyze a quantum analog of the symmetric random walk, which we call theâ€¦ (More)

We consider the possibility of encoding m classical bits into many fewer n quantum bits (qubits) so that an arbitrary bit from the original m bits can be recovered with good probability. We show thatâ€¦ (More)