Supervised learning with quantum enhanced feature spaces

Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern recognition, with support vector machines (SVMs) being the most well-known method for classification problems. However, there are limitations to the successful solution to such problems when the feature space becomes large, and the kernel functions become computationally expensive to estimate. A core element to computational speed-ups afforded by quantum algorithms is the exploitation of an exponentially large quantum state space through controllable entanglement and interference. Here, we propose and experimentally implement two novel methods on a superconducting processor. Both methods represent the feature space of a classification problem by a quantum state, taking advantage of the large dimensionality of quantum Hilbert space to obtain an enhanced solution. One method, the quantum variational classifier builds on [1,2] and operates through using a variational quantum circuit to classify a training set in direct analogy to conventional SVMs. In the second, a quantum kernel estimator, we estimate the kernel function and optimize the classifier directly. The two methods present a new class of tools for exploring the applications of noisy intermediate scale quantum computers [3] to machine learning.Comment: Fixed typos, added figures and discussion about quantum error mitigatio

Adaptive versus non-adaptive strategies for quantum channel discrimination

We provide a simple example that illustrates the advantage of adaptive over non-adaptive strategies for quantum channel discrimination. In particular, we give a pair of entanglement-breaking channels that can be perfectly discriminated by means of an adaptive strategy that requires just two channel evaluations, but for which no non-adaptive strategy can give a perfect discrimination using any finite number of channel evaluations.Comment: 11 page

Validity of discrepancy criteria for identifying children with developmental language disorders

Empirical data from two studies address the clinical validity of discrepancy criteria for identification of children with developmental language disorders (DLD). Study 1 involved 256 preschoolers clinically defined as DLD and meeting inclusionary criteria for normal hearing, intellectual, neurological, and psychiatric status. Application of alternative psychometrically derived discrepancy criteria identified only 40% to 60% of the clinically defined group as language disordered. Study 2 applied nonverbal IQ-language performance discrepancy criteria to 368 eight-year-old, randomly selected control subjects, resulting in over 45% of the controls being identified as DLD. Factors contributing to underidentification in Study 1 and overidentification in Study 2 are discussed, raising questions regarding the validity of discrepancy criteria for identification of DLD children

Wightman function and vacuum fluctuations in higher dimensional brane models

Wightman function and vacuum expectation value of the field square are evaluated for a massive scalar field with general curvature coupling parameter subject to Robin boundary conditions on two codimension one parallel branes located on $(D+1)$-dimensional background spacetime $AdS_{D_1+1}\times \Sigma$ with a warped internal space $\Sigma$. The general case of different Robin coefficients on separate branes is considered. The application of the generalized Abel-Plana formula for the series over zeros of combinations of cylinder functions allows us to extract manifestly the part due to the bulk without boundaries. Unlike to the purely AdS bulk, the vacuum expectation value of the field square induced by a single brane, in addition to the distance from the brane, depends also on the position of the brane in the bulk. The brane induced part in this expectation value vanishes when the brane position tends to the AdS horizon or AdS boundary. The asymptotic behavior of the vacuum densities near the branes and at large distances is investigated. The contribution of Kaluza-Klein modes along $\Sigma$ is discussed in various limiting cases. As an example the case $\Sigma =S^1$ is considered, corresponding to the $AdS_{D+1}$ bulk with one compactified dimension. An application to the higher dimensional generalization of the Randall-Sundrum brane model with arbitrary mass terms on the branes is discussed.Comment: 25 pages, 2 figures, discussion added, accepted for publication in Phys.Rev.

Generalized statistical models of voids and hierarchical structure in cosmology

Generalized statistical models of voids and hierarchical structure in cosmology are developed. The often quoted negative binomial model and frequently used thermodynamic model are shown to be special cases of a more general distribution which contains a parameter "a". The parameter is related to the Levy index alpha and the Fisher critical exponent tau, the latter describing the power law fall off of clumps of matter around a phase transition. The parameter"a", exponent tau, or index alpha can be obtained from properties of a void scaling function. A stochastic probability variable "p" is introduced into a statistical model which represent the adhesive growth of galaxy structure. For p<1/2, the galaxy count distribution decays exponential fast with size. For p>1/2, an adhesive growth can go on indefinitely thereby forming an infinite supercluster. At p=1/2 a scale free power law distribution for the galaxy count distribution is present. The stochastic description also leads to consequences that have some parallels with cosmic string results, percolation theory and phase transitions.Comment: 25 page

Maximizing Influence Propagation in Networks with Community Structure

We consider the algorithmic problem of selecting a set of target nodes that cause the biggest activation cascade in a network. In case when the activation process obeys the diminishing returns property, a simple hill-climbing selection mechanism has been shown to achieve a provably good performance. Here we study models of influence propagation that exhibit critical behavior, and where the property of diminishing returns does not hold. We demonstrate that in such systems, the structural properties of networks can play a significant role. We focus on networks with two loosely coupled communities, and show that the double-critical behavior of activation spreading in such systems has significant implications for the targeting strategies. In particular, we show that simple strategies that work well for homogeneous networks can be overly sub-optimal, and suggest simple modification for improving the performance, by taking into account the community structure.Comment: 7 pages, 8 figure

Adaptive Boolean Networks and Minority Games with Time--Dependent Capacities

In this paper we consider a network of boolean agents that compete for a limited resource. The agents play the so called Generalized Minority Game where the capacity level is allowed to vary externally. We study the properties of such a system for different values of the mean connectivity $K$ of the network, and show that the system with K=2 shows a high degree of coordination for relatively large variations of the capacity level.Comment: 4 pages, 4 figure

A practical scheme for quantum computation with any two-qubit entangling gate

Which gates are universal for quantum computation? Although it is well known that certain gates on two-level quantum systems (qubits), such as the controlled-not (CNOT), are universal when assisted by arbitrary one-qubit gates, it has only recently become clear precisely what class of two-qubit gates is universal in this sense. Here we present an elementary proof that any entangling two-qubit gate is universal for quantum computation, when assisted by one-qubit gates. A proof of this important result for systems of arbitrary finite dimension has been provided by J. L. and R. Brylinski [arXiv:quant-ph/0108062, 2001]; however, their proof relies upon a long argument using advanced mathematics. In contrast, our proof provides a simple constructive procedure which is close to optimal and experimentally practical [C. M. Dawson and A. Gilchrist, online implementation of the procedure described herein (2002), http://www.physics.uq.edu.au/gqc/].Comment: 3 pages, online implementation of procedure described can be found at http://www.physics.uq.edu.au/gqc

Development of a Coherent Doppler Lidar for Precision Maneuvering and Landing of Space Vehicles

A coherent Doppler lidar has been developed to address NASAs need for a high-performance, compact, and cost-effective velocity and altitude sensor onboard its landing vehicles. Future robotic and manned missions to planetary bodies require precise ground-relative velocity vector and altitude data to execute complex descent maneuvers and safe, soft landing at a pre-designated site. This lidar sensor, referred to as a Navigation Doppler Lidar, meets the required performance of landing missions while complying with vehicle size, mass, and power constraints. Operating from over five kilometers altitude, the lidar obtains velocity and range precision measurements with 2 cm/sec and 2 meters, respectively, dominated by the vehicle motion. After a series of flight tests onboard helicopters and rocket-powered free-flyer vehicles, the Navigation Doppler Lidar is now being ruggedized for future missions to various destinations in the solar system