Optimized quantum random-walk search algorithms

Shenvi, Kempe and Whaley's quantum random-walk search (SKW) algorithm [Phys. Rev. A 67, 052307 (2003)] is known to require $O(\sqrt N)$ number of oracle queries to find the marked element, where $N$ is the size of the search space. The overall time complexity of the SKW algorithm differs from the best achievable on a quantum computer only by a constant factor. We present improvements to the SKW algorithm which yield significant increase in success probability, and an improvement on query complexity such that the theoretical limit of a search algorithm succeeding with probability close to one is reached. We point out which improvement can be applied if there is more than one marked element to find.Comment: 7 pages, 2 figures. Major revision according to referee repor

Photonic quantum walks in a fiber based recursion loop

We present a flexible and robust system for implementing one-dimensional coined quantum walks. A recursion loop in the optical network together with a translation of the spatial into the time domain ensures the possible increment of the step number without need of additional optical elements. An intrinsic phase stability assures a high degree of coherence and hence guarantees a good scalability of the system. We performed a quantum walk over 27 steps and analyzed the 54 output modes. Furthermore, we estimated that up to 100 steps can be realized with only minor changes in the used components

Decoherence and disorder in quantum walks: from ballistic spread to localization

We investigate the impact of decoherence and static disorder on the dynamics of quantum particles moving in a periodic lattice. Our experiment relies on the photonic implementation of a one-dimensional quantum walk. The pure quantum evolution is characterized by a ballistic spread of a photon’s wave packet along 28 steps. By applying controlled time-dependent operations we simulate three different environmental influences on the system, resulting in a fast ballistic spread, a diffusive classical walk, and the first Anderson localization in a discrete quantum walk architecture

Quantum simulations with a two-dimensional Quantum Walk

We present an experimental implementation of a quantum walk in two dimensions, employing an optical fiber network. We simulated entangling operations and nonlinear multi-particle interactions revealing phenomena such as bound states. (C) 2011 Optical Society of Americ