We develop a new, random walk-based, algorithm for the Hamiltonian cycle problem. The random walk is on pairs of extreme points of two suitably constructed polytopes. The latter are derived from ...

Quantum walks, the quantum analogue of classical random walks, have emerged as a pivotal framework in the study of quantum dynamics and information processing. These systems exploit inherently quantum ...

Quantum walks sound abstract, but they sit at the center of a very concrete race: who will harness quantum mechanics to solve ...

Quantum Walk Algorithms Quantum walks, sometimes called quantum random walks, are quantum analogues of (classical) random walks, which have proved to be a very powerful algorithmic tool in classical ...

Random walks constitute one of the cornerstone concepts in probability theory and statistical physics, representing a class of stochastic processes in which a moving entity takes successive steps in ...