Quantum random walks have received much interest due to their nonintuitive dynamics, which may hold the key to a new generation of quantum algorithms. What remains a major challenge is a physical realization that is experimentally viable and not limited to special connectivity criteria. We present a scheme for walking on arbitrarily complex graphs, which can be realized using a variety of quantum systems such as a Bose-Einstein condensate trapped inside an optical lattice. This scheme is particularly elegant since the walker is not required to physically step between the nodes; only flipping coins is sufficient.

• Received 20 August 2008

DOI:https://doi.org/10.1103/PhysRevA.80.060304