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 sound abstract, but they sit at the center of a very concrete race: who will harness quantum mechanics to solve problems that overwhelm today’s most powerful supercomputers. Instead of ...

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 ...