  Quantum walk is a key operation in quantum computing, simulation,
communication and information. Here, we report for the first time the
demonstration of quantum walks and localized quantum walks in a new type of
optical fibers having a ring of cores constructed with both periodic and
quasiperiodic Fibonacci sequences, respectively. Good agreement between
theoretical and experimental results have been achieved. The new multicore ring
fibers provide a new platform for experiments of quantum effects in low-loss
optical fibers which is critical for scalability of real applications with
large-size problems. Furthermore, our new quasiperiodic Fibonacci multicore
ring fibers provide a new class of quasiperiodic photonics lattices possessing
both on- and off-diagonal deterministic disorders for realizing localized
quantum walks deterministically. The proposed Fibonacci fibers are simple and
straightforward to fabricate and have a rich set of properties that are of
potential use for quantum applications. Our simulation and experimental results
show that, in contrast with randomly disordered structures, localized quantum
walks in new proposed quasiperiodic photonics lattices are highly controllable
due to the deterministic disordered nature of quasiperiodic systems.
