Learning the dynamics of embedded clauses

Recent work by Siegelmann has shown that the computational power of recurrent neural networks matches that of Turing Machines. One important implication is that complex language classes (infinite languages with embedded clauses) can be represented in neural networks. Proofs are based on a fractal encoding of states to simulate the memory and operations of stacks. In the present work, it is shown that similar stack-like dynamics can be learned in recurrent neural networks from simple sequence prediction tasks. Two main types of network solutions are found and described qualitatively as dynamical systems: damped oscillation and entangled spiraling around fixed points. The potential and limitations of each solution type are established in terms of generalization on two different context-free languages. Both solution types constitute novel stack implementations - generally in line with Siegelmann's theoretical work - which supply insights into how embedded structures of languages can be handled in analog hardware.

Photon-added detection

The production of conditional quantum states and quantum operations based on the result of measurement is now seen as a key tool in quantum information and metrology. We propose a different type of photon number detector. It functions nondeterministically, but when successful, it has high fidelity. The detector, which makes use of an n-photon auxiliary Fock state and high efficiency homodyne detection, allows a tunable trade-off between fidelity and probability. By sacrificing probability of operation, an excellent approximation to a photon-number detector is achieved.

Biased EPR entanglement and its application to teleportation

We consider pure continuous variable entanglement with non-equal correlations between orthogonal quadratures. We introduce a simple protocol which equates these correlations and in the process transforms the entanglement onto a state with the minimum allowed number of photons. As an example we show that our protocol transforms, through unitary local operations, a single squeezed beam split on a beam splitter into the same entanglement that is produced when two squeezed beams are mixed orthogonally. We demonstrate that this technique can in principle facilitate perfect teleportation utilizing only one squeezed beam.

Tailoring teleportation to the quantum alphabet

We introduce a refinement of the standard continuous variable teleportation measurement and displacement strategies. This refinement makes use of prior knowledge about the target state and the partial information carried by the classical channel when entanglement is nonmaximal. This gives an improvement in the output quality of the protocol. The strategies we introduce could be used in current continuous variable teleportation experiments.

Mapping the royal road and other hierarchical functions

In this paper we present a technique for visualising hierarchical and symmetric, multimodal fitness functions that have been investigated in the evolutionary computation literature. The focus of this technique is on landscapes in moderate-dimensional, binary spaces (i.e., fitness functions defined over {0, 1}(n), for n less than or equal to 16). The visualisation approach involves an unfolding of the hyperspace into a two-dimensional graph, whose layout represents the topology of the space using a recursive relationship, and whose shading defines the shape of the cost surface defined on the space. Using this technique we present case-study explorations of three fitness functions: royal road, hierarchical-if-and-only-if (H-IFF), and hierarchically decomposable functions (HDF). The visualisation approach provides an insight into the properties of these functions, particularly with respect to the size and shape of the basins of attraction around each of the local optima.