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) …

We solve an open problem by constructing quantum walks that not only detect but also find
marked vertices in a graph. In the case when the marked set MM consists of a single vertex …

We prove that a quantum walk can detect the presence of a marked element in a graph in $
O (\sqrt {WR}) $ steps for any initial probability distribution on vertices. Here, $ W $ is the …

Spatial search by a discrete-time quantum walk can find a marked node on any ergodic,
reversible Markov chain P quadratically faster than its classical counterpart, ie, in a time that …

Szegedy's quantum walk is a quantization of a classical random walk or Markov chain,
where the walk occurs on the edges of the bipartite double cover of the original graph. To …

The quantum walk is a powerful tool to develop quantum algorithms, which usually are
based on searching for a vertex in a graph with multiple marked vertices, with Ambainis's …

We solve an open problem by constructing quantum walks that not only detect but also find
marked vertices in a graph. The number of steps of the quantum walk is quadratically …

Quantum walks play an important role in the area of quantum algorithms. Many interesting
problems can be reduced to searching marked states in a quantum Markov chain. In this …

We present two quantum walk algorithms for 3-Distinctness. Both algorithms have time
complexity ̃O(n^5/7), improving the previous ̃O(n^3/4) and matching the best known upper …

We construct a black box graph traversal problem that can be solved exponentially faster on
a quantum computer than on a classical computer. The quantum algorithm is based on a …