Quantum Searching via Entanglement and Partial Diffusion

In this paper, we will define a quantum operator that performs the inversion about the mean only on a subspace of the system (Partial Diffusion Operator). This operator is used in a quantum search algorithm that runs in O(sqrt{N/M}) for searching an unstructured list of size N with M matches such that 1<= M<=N. We will show that the performance of the algorithm is more reliable than known {fixed operators quantum search algorithms} especially for multiple matches where we can get a solution after a single iteration with probability over 90% if the number of matches is approximately more than one-third of the search space. We will show that the algorithm will be able to handle the case where the number of matches M is unknown in advance such that 1<=M<=N in O(sqrt{N/M}). A performance comparison with Grover's algorithm will be provided.Comment: 19 pages. Submitted to IJQI. Please forward comments/enquires for the first author to [email protected]

Low-temperature chemistry using the R-matrix method

Techniques for producing cold and ultracold molecules are enabling the study of chemical reactions and scattering at the quantum scattering limit, with only a few partial waves contributing to the incident channel, leading to the observation and even full control of state-to-state collisions in this regime. A new R-matrix formalism is presented for tackling problems involving low- and ultra-low energy collisions. This general formalism is particularly appropriate for slow collisions occurring on potential energy surfaces with deep wells. The many resonance states make such systems hard to treat theoretically but offer the best prospects for novel physics: resonances are already being widely used to control diatomic systems and should provide the route to steering ultracold reactions. Our R-matrix-based formalism builds on the progress made in variational calculations of molecular spectra by using these methods to provide wavefunctions for the whole system at short internuclear distances, (a regime known as the inner region). These wavefunctions are used to construct collision energy-dependent R-matrices which can then be propagated to give cross sections at each collision energy. The method is formulated for ultracold collision systems with differing numbers of atoms

The characteristic polynomial of the next-nearest-neighbour qubit chain for single excitations

The characteristic polynomial for a chain of dipole-dipole coupled two-level atoms with nearest-neighbour and next-nearest-neighbour interactions is developed for the study of eigenvalues and eigenvectors for single-photon excitations. We find the exact form of the polynomial in terms of the Chebyshev polynomials of the second kind that is valid for an arbitrary number of atoms and coupling strengths. We then propose a technique for expressing the roots of the polynomial as a power series in the coupling constants. The general properties of the solutions are also explored, to shed some light on the general properties that the exact, analytic form of the energy eigenvalues should have. A method for deriving the eigenvectors of the Hamiltonian is also outlined.Comment: 19 pages, 8 figures; minor correction

Annotating Synapses in Large EM Datasets

Reconstructing neuronal circuits at the level of synapses is a central problem in neuroscience and becoming a focus of the emerging field of connectomics. To date, electron microscopy (EM) is the most proven technique for identifying and quantifying synaptic connections. As advances in EM make acquiring larger datasets possible, subsequent manual synapse identification ({\em i.e.}, proofreading) for deciphering a connectome becomes a major time bottleneck. Here we introduce a large-scale, high-throughput, and semi-automated methodology to efficiently identify synapses. We successfully applied our methodology to the Drosophila medulla optic lobe, annotating many more synapses than previous connectome efforts. Our approaches are extensible and will make the often complicated process of synapse identification accessible to a wider-community of potential proofreaders

Approximation of Various Quantum Query Types

Query complexity measures the amount of information an algorithm needs about a problem to compute a solution. On a quantum computer there are different realizations of a query and we will show that these are not always equivalent. Our definition of equivalence is based on the ability to simulate (or approximate) one query type by another. We show that a bit query can always approximate a phase query with just two queries, while there exist problems for which the number of phase queries which are necessary to approximate a bit query must grow exponentially with the precision of the bit query. This result follows from the query complexity bounds for the evaluation problem, for which we establish a strong lower bound for the number of phase queries by exploiting a relation between quantum algorithms and trigonometric polynomials.Comment: New version. To be published in the Journal of Complexity in August. Extended by an additional sectio

Learning Arbitrary Statistical Mixtures of Discrete Distributions

We study the problem of learning from unlabeled samples very general statistical mixture models on large finite sets. Specifically, the model to be learned, $\vartheta$, is a probability distribution over probability distributions $p$, where each such $p$ is a probability distribution over $[n] = \{1,2,\dots,n\}$. When we sample from $\vartheta$, we do not observe $p$ directly, but only indirectly and in very noisy fashion, by sampling from $[n]$ repeatedly, independently $K$ times from the distribution $p$. The problem is to infer $\vartheta$ to high accuracy in transportation (earthmover) distance. We give the first efficient algorithms for learning this mixture model without making any restricting assumptions on the structure of the distribution $\vartheta$. We bound the quality of the solution as a function of the size of the samples $K$ and the number of samples used. Our model and results have applications to a variety of unsupervised learning scenarios, including learning topic models and collaborative filtering.Comment: 23 pages. Preliminary version in the Proceeding of the 47th ACM Symposium on the Theory of Computing (STOC15

Toughening and asymmetry in peeling of heterogeneous adhesives

The effective adhesive properties of heterogeneous thin films are characterized through a combined experimental and theoretical investigation. By bridging scales, we show how variations of elastic or adhesive properties at the microscale can significantly affect the effective peeling behavior of the adhesive at the macroscale. Our study reveals three elementary mechanisms in heterogeneous systems involving front propagation: (i) patterning the elastic bending stiffness of the film produces fluctuations of the driving force resulting in dramatically enhanced resistance to peeling; (ii) optimized arrangements of pinning sites with large adhesion energy are shown to control the effective system resistance, allowing the design of highly anisotropic and asymmetric adhesives; (iii) heterogeneities of both types result in front motion instabilities producing sudden energy releases that increase the overall adhesion energy. These findings open potentially new avenues for the design of thin films with improved adhesion properties, and motivate new investigation of other phenomena involving front propagation.Comment: Physical Review Letters (2012)