Abstract

As quantum systems are understood better from a fundamental physics perspective, we are gaining more insight and ideas for their many applications. Among them are quantum computation, sensing, and materials. Some difficulties that have been encountered are short lifetimes and coupling to unwanted modes while attempting to control these systems, resulting in error propagation. Previously, physicists have pursued Hermitian descriptions of systems to preserve unitary evolution and real-valued measurements. However, non-Hermitian systems not only provide a realistic description of physical systems within larger environments, but also a rich topological landscape from their complex energy spectrum. In this thesis, we will explore how to control a non-Hermitian qubit to utilize its complex spectrum and the role of its Hamiltonian in energetics and time dynamics. Because superconducting qubits offer flexibility in parameter tuning, we can tune the values of the non-Hermitian Hamiltonian to explore this complex spectrum across regions of both $\PT$-symmetry and $\PT$-symmetry breaking. This complex energy spectrum forms a Riemann surface that has a branch cut and branch points (exceptional points). Encircling these exceptional points adiabatically allows for state transport that can non-trivially convert between eigenstates. Previous experimental studies of this process revealed a chirality: eigenstate conversion occurs when following the state with higher gain, but breaks down when following the state with higher loss. We explore how the interplay between gain and loss in modes of the system results in the breakdown of this adiabaticity and how we can use a method based on shortcuts to adiabaticity to circumvent this. Finally, we leverage this tunability to further investigate how the components of the non-Hermitian Hamiltonian relate to classical thermodynamic notions of internal energy and work in time-dependent protocols via the Jarzynski equality.

Committee Chair

Kater Murch

Committee Members

Aravind Nagulu; Erik Henriksen; Karthik Ramanathan; Matthew Lew

Degree

Doctor of Philosophy (PhD)

Author's Department

Electrical & Systems Engineering

Author's School

McKelvey School of Engineering

Document Type

Dissertation

Date of Award

11-4-2025

Language

English (en)

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