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 problems that overwhelm today’s most powerful supercomputers. Instead of ...

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 ...