Analog Emulation of Hyperbolic Space with and Coherence Effects in Superconducting Circuits

Abstract

Superconducting circuits, recognized by the 2025 Nobel Prize in Physics, have become a leading platform for physics simulation, quantum computation, and advanced materials research. This thesis advances both physics emulation and coherence characterization within this framework.

The first part presents a scalable superconducting-circuit architecture for studying physics dynamics on non-Euclidean lattices. By using high-quality semi-lumped coplanar waveguide resonators with carefully engineered capacitive couplings, we implement tight-binding networks whose connectivity cannot be embedded in Euclidean space. This enables the experimental realization of three distinct lattices: the {8, 3} hyperbolic lattice, a kagome-like variant, and a {12, 4} lattice whose fundamental domain resides on a genus-3 Riemann surface. Measurements reveal features predicted by hyperbolic band theory, including a macroscopically degenerate flat-band ground state and clear differentiation between Euclidean and hyperbolic connectivity.

Next, the thesis explores coherence phenomena theoretically, focusing on the rapid generation of non-classical states relevant to bosonic quantum computing. A fast protocol is proposed to generate Schrodinger cat states in a resonator using a continuously driven qubit, without relying on the dispersive regime, Kerr nonlinearity, or engineered dissipation. Analysis in the resonant regime reveals that the cat-state size grows quadratically with time, and the method is extended to weakly anharmonic qutrits, making it applicable to transmon qubits.

The final part examines noise and decoherence in superconducting qubits through long-duration purity benchmarking experiments. These measurements separately quantify coherent and incoherent error processes and reveal strong frequency dependence and telegraphic fluctuations that are consistent with coupling to individual two-level defects (TLSs).

Additional multi-qubit characterization experiments, presented in the appendices, document the fabrication, calibration, and device-level procedures underlying the main projects. Altogether, this thesis demonstrates how engineered superconducting resonators and qubits can be used to emulate physics dynamics on curved geometries, generate useful nonclassical microwave states, and probe noise mechanisms, providing a unified experimental foundation for future circuit-based quantum technologies.