Quantum Algorithms: Entanglement Enhanced Information Processing

We discuss the fundamental role of entanglement as the essential nonclassical feature providing the computational speed-up in the known quantum algorithms. We review the construction of the Fourier transform on an Abelian group and the principles underlying the fast Fourier transform algorithm. We describe the implementation of the FFT algorithm for the group of integers modulo 2^n in the quantum context, showing how the group-theoretic formalism leads to the standard quantum network and identifying the property of entanglement that gives rise to the exponential speedup (compared to the classical FFT). Finally we outline the use of the Fourier transform in extracting periodicities, which underlies its utility in the known quantum algorithms.Comment: 17 pages latex, no figures. To appear in Phil. Trans. Roy. Soc. (Lond.) 1998, Proceedings of Royal Society Discussion Meeting ``Quantum Computation: Theory and Experiment'', held in November 199

Nuclear Quantum Effects in Water and Aqueous Systems: Experiment, Theory, and Current Challenges

Nuclear quantum effects influence the structure and dynamics of hydrogen-bonded systems, such as water, which impacts their observed properties with widely varying magnitudes. This review highlights the recent significant developments in the experiment, theory, and simulation of nuclear quantum effects in water. Novel experimental techniques, such as deep inelastic neutron scattering, now provide a detailed view of the role of nuclear quantum effects in water's properties. These have been combined with theoretical developments such as the introduction of the principle of competing quantum effects that allows the subtle interplay of water's quantum effects and their manifestation in experimental observables to be explained. We discuss how this principle has recently been used to explain the apparent dichotomy in water's isotope effects, which can range from very large to almost nonexistent depending on the property and conditions. We then review the latest major developments in simulation algorithms and theory that have enabled the efficient inclusion of nuclear quantum effects in molecular simulations, permitting their combination with on-the-fly evaluation of the potential energy surface using electronic structure theory. Finally, we identify current challenges and future opportunities in this area of research

Rapid Visual Categorization is not Guided by Early Salience-Based Selection

The current dominant visual processing paradigm in both human and machine research is the feedforward, layered hierarchy of neural-like processing elements. Within this paradigm, visual saliency is seen by many to have a specific role, namely that of early selection. Early selection is thought to enable very fast visual performance by limiting processing to only the most salient candidate portions of an image. This strategy has led to a plethora of saliency algorithms that have indeed improved processing time efficiency in machine algorithms, which in turn have strengthened the suggestion that human vision also employs a similar early selection strategy. However, at least one set of critical tests of this idea has never been performed with respect to the role of early selection in human vision. How would the best of the current saliency models perform on the stimuli used by experimentalists who first provided evidence for this visual processing paradigm? Would the algorithms really provide correct candidate sub-images to enable fast categorization on those same images? Do humans really need this early selection for their impressive performance? Here, we report on a new series of tests of these questions whose results suggest that it is quite unlikely that such an early selection process has any role in human rapid visual categorization.Comment: 22 pages, 9 figure

Theory-driven learning : using intra-example relationships to constrain learning

We describe an incremental learning algorithm, called theory-driven learning, that creates rules to predict the effect of actions. Theory-driven learning exploits knowledge of regularities among rules to constrain the learning problem. We demonstrate that this knowledge enables the learning system to rapidly converge on accurate predictive rules and to tolerate more complex training data. An algorithm for incrementally learning these regularities is described and we provide evidence that the resulting regularities are sufficiently general to facilitate learning in new domains