Multidimensional quantum walks can exhibit highly nontrivial topological structure, providing a powerful tool for simulating quantum information and transport systems. We present a flexible implementation of a two-dimensional (2D) optical quantum walk on a lattice, demonstrating a scalable quantum walk on a nontrivial graph structure. We realized a coherent quantum walk over 12 steps and 169 positions by using an optical fiber network. With our broad spectrum of quantum coins, we were able to simulate the creation of entanglement in bipartite systems with conditioned interactions. Introducing dynamic control allowed for the investigation of effects such as strong nonlinearities or two-particle scattering. Our results illustrate the potential of quantum walks as a route for simulating and understanding complex quantum systems.

SummaryHeterosis is broadly de®ned as the increased vigour of hybrids in comparison to their parents. In the model plant Arabidopsis thaliana, a signi®cant heterosis effect on leaf-freezing tolerance was observed in the F 1 generation of a cross between the accessions Columbia-0 (Col) and C24. Parental Col plants were signi®-cantly more freezing-tolerant than C24 plants in both the acclimated and non-acclimated (NA) states. Midparent heterosis was observed in the F 1 plants, both in the basic tolerance of non-adapted plants and in freezing tolerance after cold acclimation. Best-parent heterosis, on the other hand, was only found after cold acclimation. The heterosis effect was reduced in the F 2 populations such that only mid-parent heterosis was evident. The leaf content of soluble sugars (fructose (Fru), glucose (Glc), sucrose (Suc) and raf®nose (Raf)) increased dramatically in the F 1 plants after cold acclimation as compared to the parental lines. The content of proline (Pro), however, was only moderately increased in the F 1 plants under the same conditions. Correlation analyses showed that only Raf content was consistently related to leaf-freezing tolerance in both the acclimated and NA states. A quanti®cation of mRNA levels in leaves of parental and F 1 lines using quantitative real-time RT-PCR showed no clear indication for an involvement of the investigated genes (CBF (C-repeat binding factor)1, CBF2, (cold-regulated protein (COR ) 6.6, COR15a, COR15b, COR47 and COR78 ) in the heterosis effect.

We present an architecture for arbitrarily scalable boson sampling using two nested fiber loops. The architecture has fixed experimental complexity, irrespective of the size of the desired interferometer, whose scale is limited only by fiber and switch loss rates. The architecture employs time-bin encoding, whereby the incident photons form a pulse train, which enters the loops. Dynamically controlled loop coupling ratios allow the construction of the arbitrary linear optics interferometers required for boson sampling. The architecture employs only a single point of interference and may thus be easier to stabilize than other approaches. The scheme has polynomial complexity and could be realized using demonstrated present-day technologies.