The key idea is that the hitting times of the random walk provide a random function for which no algorithm can locate the minimum within 2 d (1/2 - ε) steps. The purpose of The Annals of Probability ...

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 ...

We also find new equilibria by implementing two versions of a random walk algorithm. First, we cluster sub-groups of particles into patterns during the packing process, and 'grow' a packed state using ...

The lab has also designed a simple algorithm that encodes recognition between cargos and their destinations, and allows for a simple robot design.

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 walks are changing the way scientists think about computation. They use the strange and powerful rules of quantum physics—such as superposition, interference, and entanglement—to solve ...