Abstract
Large-scale population dynamics governed by ensemble systems present significant challenges due to their inherently high dimensionality. Recent advances have demonstrated the effectiveness of moment-based methods (particularly those employing polynomial bases such as Legendre and Chebyshev polynomials) when integrated with optimization techniques for control design in ensemble systems. However, these methods have not been extensively explored for enhancing robustness against systematic noise, nor have they been widely applied to complex quantum systems involving multi-parameter configurations and entanglement phenomena. In this work, we extend the application of moment methods in ensemble systems through two projects. Initially by developing a Kalman filter analogue, achieved through the decomposition of systematic stochastic processes into their corresponding moments. The resulting methodology enables sub-optimal noise filtering while significantly reducing computational cost via dimensionality reduction. Furthermore, we apply optimal Hamiltonian engineering to quantum systems characterized by parameterized inhomogeneities. Our first application involves the matter-wave splitting of a Bose-Einstein Condensate (BEC) under experimental imperfections and initial momentum dispersion, demonstrating increased fidelity and improved performance for quantum metrology. Additionally, we employ this approach in a quantum network of two-level systems (e.g. qubits, spin particles, ...) governed by the symmetric Ising model. These tensor-network-driven dynamics are simulated, and optimized pulse sequences are generated for the robust preparation of entangled symmetric states, including GHZ and W states, which are crucial for high-precision quantum sensing.
Committee Chair
Jr-Shin Li
Committee Members
Anatoly Zlotnik; Shen Zeng; ShiNung Ching; Xudong Chen
Degree
Doctor of Philosophy (PhD)
Author's Department
Electrical & Systems Engineering
Document Type
Dissertation
Date of Award
8-18-2025
Language
English (en)
DOI
https://doi.org/10.7936/n5g3-h141
Recommended Citation
Paes de Lima, Andre Luiz, "Moment Ensemble Approaches for Estimation and Robust Quantum Control" (2025). McKelvey School of Engineering Theses & Dissertations. 1288.
The definitive version is available at https://doi.org/10.7936/n5g3-h141