FLUXONIUM-BASED QUANTUM PROCESSORS AND ELECTROMAGNETIC DESIGN FOR SUPERCONDUCTING QUANTUM HARDWARE

Abstract

Quantum computing seeks to exploit coherent quantum dynamics, entanglement, and measurement to perform information-processing tasks that are intractable for classical computers. Realizing this goal requires physical qubits that combine long coherence, high-fidelity control and readout, reproducible fabrication, and scalable integration. Superconducting circuits are a leading platform because their parameters can be set lithographically, their interactions can be shaped through microwave engineering, and their control is natively compatible with established cryogenic measurement infrastructure. This dissertation concerns the modeling, validation, and design of fluxonium-based superconducting processors. Fluxonium's large inductive shunt and strong anharmonicity allow its multi-level spectrum, transition matrix elements, and noise sensitivities to be engineered across a broad range of operating regimes, offering long coherence, protected transitions, and hardware-efficient gates. These same features, however, make a fluxonium processor demanding to model, and scalable design therefore requires quantitative Hamiltonians that connect circuit geometry, the electromagnetic environment, effective parameters, and measured performance. The organizing principle of this work is that such a Hamiltonian earns its name only if, once its parameters are fixed by spectroscopy, it also predicts observables to which it was never fit. The first part develops a circuit-modeling framework for fluxonium and coupled-fluxonium systems. Beginning from circuit topology and node-flux analysis, Lagrangians and Hamiltonians are derived for single-fluxonium circuits and for inductively coupled fluxoniums sharing a common junction, yielding a consistent parameterization in terms of Josephson, inductive, and charging energies. For the coupled device, the full analysis reveals an additional collective $LC$ mode generated by capacitive cross-talk, which a minimal two-qubit model omits but the measured spectrum requires. The second part validates these Hamiltonians against experiment for two representative devices: a single fluxonium operated at integer flux, where a transmon-comparable transition frequency is combined with a suppressed charge matrix element and reduced dielectric loss, and a shared-inductance coupled-fluxonium operated at half flux, where a static mutual inductance hybridizes the computational subspace strongly enough for a large microwave-activated conditional interaction while keeping the always-on $ZZ$ interaction at the kilohertz level. In each case a single spectroscopically fixed Hamiltonian reproduces the transition matrix elements, coherence budget, conditional drive rates, and gate-error structure it was not fit to. Independent characterization and randomized benchmarking demonstrate high-fidelity operation, including a two-qubit CNOT gate with fidelity exceeding 99.9% maintained over a 24-day period. The third part extends the workflow from idealized circuit graphs to layout-aware electromagnetic extraction. An impedance-based procedure converts full-wave electromagnetic simulation data into effective qubit-qubit coupling estimates; implemented within a commercial electromagnetic environment and benchmarked against a reconstructed IBM 16-qubit transmon processor, it reproduces the reported nearest-neighbor couplings to within 6--14%. The transmon benchmark is chosen to leverage public device data, but the methodology establishes a general framework for translating physical layouts into Hamiltonian parameters, and the linear-environment step it validates is common to both modalities. Finally, this dissertation synthesizes these theoretical and experimental results and closes with a broader outlook on electromagnetic-to-Hamiltonian workflows for fluxonium, fluxonium spin-chain simulation, and hardware-informed pulse-level control. The central conclusion is that accurate circuit quantization, experimentally constrained parameter extraction, and layout-aware electromagnetic simulation must be systematically unified to build reliable, high-fidelity superconducting quantum processors.