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 ...

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 ...

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 ...

Single atoms have been spotted doing the quantum version of the random walk by physicists in Germany. This sighting of a “quantum walk” could help in the design of quantum search algorithms, or in the ...

Quantum bits (qubits) are the building blocks of quantum computers, but putting enough of them together in the one device to run computations like those expected in a standard computer is difficult to ...