ESE Ph.D. Thesis Defense: “Design and control of dynamical systems: a classical to quantum perspective”

The design and control of dynamical systems have long been core objectives of engineering. In this thesis, we tackle the complexities of design and control across paradigms ranging from Boolean models of genetic networks, to thermally driven stochastic systems, to quantum-mechanical systems. These disparate domains share common challenges, including the large dimensionality of the design space and the computational intractability of objective functions. For classical systems, we draw inspiration from optimization heuristics and genetic programming, leveraging the inherent symmetries within these problems. This approach led to the discovery of a novel symmetry in biological systems, which we term dynamical mirror symmetry, and the subsequent design of artificial mechanical structures that emulate the behavior of biological prions. Quantum systems introduce an additional layer of complexity: the exponential growth in the dimensionality of the Hilbert space, which makes classical simulations impractical. As a test platform, we develop control sequences tailored for nitrogen vacancy centers to achieve precise control. Our approach begins with the use of standardized quantum control sequences, demonstrating their capability to infer the parameters of a quantum Hamiltonian. We then develop a more general method inspired by diagrammatic path integrals, which enables full differentiability and supports perturbative expansions for optimization and control.