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University of New Mexico

1. Baldwin, Charles. Efficient and Robust Methods for Quantum Tomography.

Degree: Physics & Astronomy, 2016, University of New Mexico

URL: https://digitalrepository.unm.edu/phyc_etds/105

The development of large-scale platforms that implement quantum information processing protocols requires new methods for verification and validation of quantum behavior. Quantum tomography (QT) is the standard tool for diagnosing quantum states, process, and readout devices by providing complete information about each. However, QT is limited since it is expensive to not only implement experimentally, but also requires heavy classical post-processing of experimental data. In this dissertation, we introduce new methods for QT that are more efficient to implement and robust to noise and errors, thereby making QT a more widely practical tool for current quantum information experiments. The crucial detail that makes these new, efficient, and robust methods possible is prior information about the quantum system. This prior information is prompted by the goals of most experiments in quantum information. Most quantum information processing protocols require pure states, unitary processes, and rank-1 POVM operators. Therefore, most experiments are designed to operate near this ideal regime, and have been tested by other methods to verify this objective. We show that when this is the case, QT can be accomplished with significantly fewer resources, and produce a robust estimate of the state, process, or readout device in the presence of noise and errors. Moreover, the estimate is robust even if the state is not exactly pure, the process is not exactly unitary, or the POVM is not exactly rank-1. Such compelling methods are only made possible by the positivity constraint on quantum states, processes, and POVMs. This requirement is an inherent feature of quantum mechanics, but has powerful consequences to QT. Since QT is necessarily an experimental tool for diagnosing quantum systems, we discuss a test of these new methods in an experimental setting. The physical system is an ensemble of laser-cooled cesium atoms in the laboratory of Prof. Poul Jessen. The atoms are prepared in the hyperfine ground manifold, which provides a large, 16-dimensional Hilbert space to test QT protocols. Experiments were conducted by Hector Sosa-Martinez et al. to demonstrate different QT protocols. We compare the results, and conclude that the new methods are effective for QT.
*Advisors/Committee Members: Deutsch, Ivan, Jessen, Poul, Francisco, Becerra, Caves, Carl.*

Subjects/Keywords: Quantum tomography; Quantum information; Atomic physics; Physics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Baldwin, C. (2016). Efficient and Robust Methods for Quantum Tomography. (Doctoral Dissertation). University of New Mexico. Retrieved from https://digitalrepository.unm.edu/phyc_etds/105

Chicago Manual of Style (16^{th} Edition):

Baldwin, Charles. “Efficient and Robust Methods for Quantum Tomography.” 2016. Doctoral Dissertation, University of New Mexico. Accessed October 26, 2020. https://digitalrepository.unm.edu/phyc_etds/105.

MLA Handbook (7^{th} Edition):

Baldwin, Charles. “Efficient and Robust Methods for Quantum Tomography.” 2016. Web. 26 Oct 2020.

Vancouver:

Baldwin C. Efficient and Robust Methods for Quantum Tomography. [Internet] [Doctoral dissertation]. University of New Mexico; 2016. [cited 2020 Oct 26]. Available from: https://digitalrepository.unm.edu/phyc_etds/105.

Council of Science Editors:

Baldwin C. Efficient and Robust Methods for Quantum Tomography. [Doctoral Dissertation]. University of New Mexico; 2016. Available from: https://digitalrepository.unm.edu/phyc_etds/105

University of New Mexico

2. Shrestha, Munik. Statistics of Epidemics in Networks by Passing Messages.

Degree: Physics & Astronomy, 2016, University of New Mexico

URL: http://hdl.handle.net/1928/31743

Epidemic processes are common out-of-equilibrium phenomena of broad interdisciplinary interest. In this thesis, we show how message-passing approach can be a helpful tool for simulating epidemic models in disordered medium like networks, and in particular for estimating the probability that a given node will become infectious at a particular time. The sort of dynamics we consider are stochastic, where randomness can arise from the stochastic events or from the randomness of network structures. As in belief propagation, variables or messages in message-passing approach are defined on the directed edges of a network. However, unlike belief propagation, where the posterior distributions are updated according to Bayes' rule, in message-passing approach we write differential equations for the messages over time. It takes correlations between neighboring nodes into account while preventing causal signals from backtracking to their immediate source, and thus avoids "echo chamber effects" where a pair of adjacent nodes each amplify the probability that the other is infectious. In our first results, we develop a message-passing approach to threshold models of behavior popular in sociology. These are models, first proposed by Granovetter, where individuals have to hear about a trend or behavior from some number of neighbors before adopting it themselves. In thermodynamic limit of large random networks, we provide an exact analytic scheme while calculating the time dependence of the probabilities and thus learning about the whole dynamics of bootstrap percolation, which is a simple model known in statistical physics for exhibiting discontinuous phase transition. As an application, we apply a similar model to financial networks, studying when bankruptcies spread due to the sudden devaluation of shared assets in overlapping portfolios. We predict that although diversification may be good for individual institutions, it can create dangerous systemic effects, and as a result financial contagion gets worse with too much diversification. We also predict that financial system exhibits "robust yet fragile" behavior, with regions of the parameter space where contagion is rare but catastrophic whenever it occurs. In further results, we develop a message-passing approach to recurrent state epidemics like susceptible-infectious-susceptible and susceptible-infectious-recovered-susceptible where nodes can return to previously inhabited states and multiple waves of infection can pass through the population. Given that message-passing has been applied exclusively to models with one-way state changes like susceptible-infectious and susceptible-infectious-recovered, we develop message-passing for recurrent epidemics based on a new class of differential equations and demonstrate that our approach is simple and efficiently approximates results obtained from Monte Carlo simulation, and that the accuracy of message-passing is often superior to the pair approximation (which also takes second-order correlations into account).
*Advisors/Committee Members: Moore, Cris, Moore, Cris, Caves, Carl, Roy, Mousumi, Dunlap, David.*

Subjects/Keywords: Statistics; Epidemics; Networks; Message Passing

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Shrestha, M. (2016). Statistics of Epidemics in Networks by Passing Messages. (Doctoral Dissertation). University of New Mexico. Retrieved from http://hdl.handle.net/1928/31743

Chicago Manual of Style (16^{th} Edition):

Shrestha, Munik. “Statistics of Epidemics in Networks by Passing Messages.” 2016. Doctoral Dissertation, University of New Mexico. Accessed October 26, 2020. http://hdl.handle.net/1928/31743.

MLA Handbook (7^{th} Edition):

Shrestha, Munik. “Statistics of Epidemics in Networks by Passing Messages.” 2016. Web. 26 Oct 2020.

Vancouver:

Shrestha M. Statistics of Epidemics in Networks by Passing Messages. [Internet] [Doctoral dissertation]. University of New Mexico; 2016. [cited 2020 Oct 26]. Available from: http://hdl.handle.net/1928/31743.

Council of Science Editors:

Shrestha M. Statistics of Epidemics in Networks by Passing Messages. [Doctoral Dissertation]. University of New Mexico; 2016. Available from: http://hdl.handle.net/1928/31743

University of New Mexico

3. Chase, Bradley. Parameter estimation, model reduction and quantum filtering.

Degree: Physics & Astronomy, 2010, University of New Mexico

URL: http://hdl.handle.net/1928/10340

This thesis explores the topics of parameter estimation and model reduction in the context of quantum filtering. The last is a mathematically rigorous formulation of continuous quantum measurement, in which a stream of auxiliary quantum systems is used to infer the state of a target quantum system. Fundamental quantum uncertainties appear as noise which corrupts the probe observations and therefore must be filtered in order to extract information about the target system. This is analogous to the classical filtering problem in which techniques of inference are used to process noisy observations of a system in order to estimate its state. Given the clear similarities between the two filtering problems, I devote the beginning of this thesis to a review of classical and quantum probability theory, stochastic calculus and filtering. This allows for a mathematically rigorous and technically adroit presentation of the quantum filtering problem and solution. Given this foundation, I next consider the related problem of quantum parameter estimation, in which one seeks to infer the strength of a parameter that drives the evolution of a probe quantum system. By embedding this problem in the state estimation problem solved by the quantum filter, I present the optimal Bayesian estimator for a parameter when given continuous measurements of the probe system to which it couples. For cases when the probe takes on a finite number of values, I review a set of sufficient conditions for asymptotic convergence of the estimator. For a continuous-valued parameter, I present a computational method called quantum particle filtering for practical estimation of the parameter. Using these methods, I then study the particular problem of atomic magnetometry and review an experimental method for potentially reducing the uncertainty in the estimate of the magnetic field beyond the standard quantum limit. The technique involves double-passing a probe laser field through the atomic system, giving rise to effective non-linearities which enhance the effect of Larmor precession allowing for improved magnetic field estimation. I then turn to the topic of model reduction, which is the search for a reduced computational model of a dynamical system. This is a particularly important task for quantum mechanical systems, whose state grows exponentially in the number of subsystems. In the quantum filtering setting, I study the use of model reduction in developing a feedback controller for continuous-time quantum error correction. By studying the propagation of errors in a noisy quantum memory, I present a computation model which scales polynomially, rather than exponentially, in the number of physical qubits of the system. Although inexact, a feedback controller using this model performs almost indistinguishably from one using the full model. I finally review an exact but polynomial model of collective qubit systems undergoing arbitrary symmetric dynamics which allows for the efficient simulation of spontaneous-emission and related open quantum system…
*Advisors/Committee Members: Geremia, JM, Landahl, Andrew, Deutsch, Ivan, Caves, Carl.*

Subjects/Keywords: Quantum statistics; Parameter estimation; Stochastic analysis; Magnetic fields – Measurement; Feedback control systems – Mathematical models.

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Chase, B. (2010). Parameter estimation, model reduction and quantum filtering. (Doctoral Dissertation). University of New Mexico. Retrieved from http://hdl.handle.net/1928/10340

Chicago Manual of Style (16^{th} Edition):

Chase, Bradley. “Parameter estimation, model reduction and quantum filtering.” 2010. Doctoral Dissertation, University of New Mexico. Accessed October 26, 2020. http://hdl.handle.net/1928/10340.

MLA Handbook (7^{th} Edition):

Chase, Bradley. “Parameter estimation, model reduction and quantum filtering.” 2010. Web. 26 Oct 2020.

Vancouver:

Chase B. Parameter estimation, model reduction and quantum filtering. [Internet] [Doctoral dissertation]. University of New Mexico; 2010. [cited 2020 Oct 26]. Available from: http://hdl.handle.net/1928/10340.

Council of Science Editors:

Chase B. Parameter estimation, model reduction and quantum filtering. [Doctoral Dissertation]. University of New Mexico; 2010. Available from: http://hdl.handle.net/1928/10340