Computer Science Approach to Quantum Control

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The spectrum of applications is huge, going from financial forecasting to medical diagnosis to industrial inspection to recommendation systems, to name a few. The field encompasses neural networks, statistical inference, and data mining. Professor Anandkumar's research interests are in the areas of large-scale machine learning, non-convex optimization and high-dimensional statistics.

In particular, she has been spearheading the development and analysis of tensor algorithms for machine learning. Tensor decomposition methods are embarrassingly parallel and scalable to enormous datasets. They are guaranteed to converge to the global optimum and yield consistent estimates for many probabilistic models such as topic models, community models, and hidden Markov models.

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More generally, Professor Anandkumar has been investigating efficient techniques to speed up non-convex optimization such as escaping saddle points efficiently. Professor Barr's research involves 1 mathematical simulation methods for computer graphics 2 developing new types of mathematical and computational methods for the study of biophysical behaviors and structures, and 3 technological leveraging for medical health care and new medical devices.

In addition, he has been collaborating with JPL researcher Dr. Martin Lo on new computational and mathematical methods for utilizing the InterPlanetary Superhighway for developing new missions in the Solar System. All of these research areas involve the development and application of new mathematical and computational methods in the context of new applications in the physical sciences. Katie Bouman's research focuses on computational imaging: designing systems that tightly integrate algorithm and sensor design, making it possible to observe phenomena previously difficult or impossible to measure with traditional approaches.

Imaging plays a critical role in advancing science. However, as science continues to push boundaries, traditional sensors are reaching the limits of what they can measure. Katie's group combines ideas from signal processing, computer vision, machine learning, and physics to find and exploit hidden signals for both scientific discovery and technological innovation.

Intelligent control systems. I. Quantum computing and self-organization algorithm | SpringerLink

For example, in collaboration with the Event Horizon Telescope, Katie's group is helping to build a computational earth-sized telescope that is taking the first images of a black hole and is analyzing its images to learn about general relativity in the strong-field regime. Bruno's work focuses on development of accurate, high-performance numerical PDE solvers capable of modeling faithfully realistic scientific and engineering configurations.

How Quantum Computers Break Encryption - Shor's Algorithm Explained

Recently developed Fourier Continuation FC and integral-equation techniques, which can successfully tackle such challenges, have enabled accurate solution of previously intractable PDE problems of fundamental importance in science and engineering. Richard L. Professor Burdick focuses on robotics, kinematics, mechanical systems and control.

Active research areas include: robotic locomotion, sensor-based motion planning algorithms, multi-fingered robotic manipulation, applied nonlinear control theory, neural prosthetics, and medical applications of robotics. Specific areas of interest include convex optimization, mathematical signal processing, graphs and combinatorial optimization, applied algebraic geometry, computational harmonic analysis, and statistical inference.

Applied geometry geometry processing, meshing, and computer graphics ; Discrete differential modeling differential, yet readily-discretizable tools for computational modeling ; finite element modeling. Doyle's research is on theoretical foundations for complex tech, bio, med, neuro, and social networks integrating control, communications, computing, and multiscale physics. Layered architectures such as brains integrate high level planning with fast lower level sensing, reflex, and action and facilitate learning, adaptation, augmentation tools , and teamwork, despite being implemented in energy efficient hardware with sparse, quantized, noisy, delayed, and saturating sensing, communications, computing, and actuation, on time scales from milliseconds to minutes to days.

We are developing a mathematical framework that deals with all of these features and constraints in a coherent and rigorous way with broad applications in science, technology, ecology, and society. Professor Hou focuses on multiscale problems arising from geophysical applications and fluid dynamics, the Millennium Problem on the 3D incompressible Navier-Strokes equations, model reduction for stochastic problems with high dimensional input variables, and adaptive data analysis.

Professor Meiron's research focuses on computation and modelling of basic fluid mechanical phenomena. Particular interests include shock driven flow instabilities, turbulence, simulation approaches for high strain rate solid mechanics.

Research areas

He is also interested on development of adaptive numeriocal methods for such flows that are suitable for high performance computation. Thomas E. Research in Richard Murray's group is in the application of feedback and control to networked systems, with applications in biology and autonomy. Current projects include novel control system architectures, biomolecular feedback systems and networked control systems. Professor Patcher is a computational biologist working in genomics.

Research provides speed boost to quantum computers

His career began in comparative genomics, and initially was interested in genome alignment, annotation, and the determination of conserved regions using phylogenetic methods. More recently he's become focused on functional genomics, which includes answering questions about the function and interaction of DNA, RNA and protein products. He's particularly interested in applications of high-throughput sequencing to RNA biology. Genomics requires the development of algorithms, statistical methodology and mathematical foundations, and a major part of his research is therefore on methods.

Engineering small conditional DNAs and RNAs for signal transduction in vitro, in situ, and in vivo; computational algorithms for the analysis and design of nucleic acid structures, devices, and systems; programmable molecular technologies for readout and regulation of the state of endogenous biological circuitry. These range from geometric modeling effective methods to model the shape of objects to animation simulation of physical phenomena such as the deformation of cloth. His emphasis is on an area known as "Discrete Differential Geometry. Professor Stuart's research is focused on the development of mathematical and algorithmic frameworks for the seamless integration of models with data.

He works in the Bayesian formulation of inverse problems, and in data assimilation for dynamical systems. Quantification of uncertainty plays a significant role in this work. Current applications of interest include a variety of problems in the geophysical sciences, and in graph-based learning. Joel Tropp's work lies at the interface of applied mathematics, electrical engineering, computer science, and statistics. This research concerns the theoretical and computational aspects of data analysis, sparse modeling, randomized linear algebra, and random matrix theory. Professor Umans is interested in theoretical computer science, and especially computational complexity.

He enjoys problems with an algebraic flavor, and this often leads to research questions in derandomization and explicit combinatorial constructions, algebraic algorithms, coding theory, and hardness of approximation. He is interested in applying techniques from computer science, such as complexity theory, to study problems in quantum computing.

He has investigated the role of entanglement in multi-prover interactive proof systems and obtained the first substantial computational hardness results on the power of entangled provers. Entanglement also plays a major role in quantum cryptography, and he has made important contributions to the field of device-independent cryptography. He is also interested in using quantum information theory to shed new light on fundamental techniques in theoretical computer science such as semidefinite programming and approximation algorithms. Adam Wierman's research interests center around resource allocation and scheduling decisions in computer systems and services.

More specifically, his work focuses both on developing analytic techniques in stochastic modeling, optimization, machine learning, and game theory, and applying these techniques to application domains such as energy-efficient computing, the cloud, the smart grid, and social networks. Professor Winfree's research involves theoretical and experimental aspects of molecular programming. Models of computation are developed that incorporate essential features of molecular folding, molecular self-assembly, biochemical circuits, and molecular robotics.

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  • These models are studied to determine their expressiveness for programming molecular-level tasks including decision-making, memory, behavior, and morphogenesis. Methods for compiling abstract molecular programs into actual molecules are developed and tested in the laboratory. Yisong Yue's research interests lie primarily in the theory and application of statistical machine learning. He is particularly interested in developing novel methods for interactive machine learning and structured machine learning. He explores the interplay of physics, computer science and mathematics to study the role of quantum mechanics in computation and information transmission.

    In recent years he has been exploring several directions in entanglement theory, from understanding the relation between entanglement and other physical properties such as correlation length in quantum many-body systems, to developing a sharper understanding of fundamental properties of entanglement such as its monogamous character with applications in quantum cryptography, quantum Hamiltonian complexity, and even in convex optimisation. Professor Chung's research focuses on distributed spacecraft systems, space autonomous systems, and aerospace robotics, and in particular, on the theory and application of complex nonlinear dynamics, control, estimation, guidance, and navigation of autonomous space and air vehicles.

    Frederick Eberhardt's research interests lie at the formal end of philosophy of science, the machine learning end of statistics and computer science, and the learning and modeling end of psychology and cognitive science. His work has focused primarily on methods for causal discovery from statistical data, the use of experiments in causal discovery, the integration of causal inferences from different data sets and the philosophical issues at the foundations of causality and probability.

    He has done some work on computational models in cognitive science and some historical work on the philosophy of Hans Reichenbach, especially his frequentist interpretation of probability. Mose and Lillian S. Hassibi's research spans various aspects of information theory, signal processing, control theory, and machine learning.

    He has made contributions to the theory and practice of wireless communications and wireless networks, as well as to robust control, adaptive filtering and neural networks, network information theory, coding for control, phase retrieval, structured signal recovery, high dimensional statistics, epidemic spread in complex networks, and DNA micro-arrays. Professor Kitaev works in the field of quantum computation and related areas of theoretical physics. His main contribution was the concept of topological quantum computation, a scheme where quantum information is protected from errors due to special properties of the underlying physical system, which are generally related to topology.

    He currently focuses on topological classification of quantum phases a nontrivial example being the 2-dimensional electron liquid in the quantum Hall regime.