This dissertation explores quantum computing applications of fluxonium superconductingcircuits. Fluxonium’s high coherence time T2 and anharmonicity make it an excellent platform for both digital quantum processors and analog quantum simulators. Focusing on the digital quantum computing applications, we report recent work on improving the T2 and gate error rates of fluxonium qubits. Through enhancements in fabrication methods and engineering of fluxonium’s spectrum, a coherence time in excess of 1 millisecond is achieved, setting a new standard for the most coherent superconducting qubit. This highly coherent device is used to demonstrate a single-qubit gate fidelity greater than 99.99%, a level of control that had not been observed until now in a solid state quantum system. Utilizing the high energy relaxation time T1 of the qubit transition, a novel measurement of the circuit’s parity-protected 0-2 transition relaxation time is performed to extract additional sources of energy loss.

To demonstrate fluxonium’s utility as a building block for analog quantum simulators,we investigate how to simulate quantum dynamics in the Transverse-Field Ising Model (TFIM) by inductively coupling 10 fluxonium circuits together. When the fluxonium loops are biased at half integer values of the magnetic flux quantum, the spectrum is highly anharmonic, and the qubit transition is well-approximated by a spin-1/2. This results in an effective Hamiltonian that is equivalent to the TFIM. By tuning the inter-qubit coupling across multiple devices, we can explore different regimes of the TFIM, establishing fluxonium as a prominent candidate for use in near-term quantum many-body simulations.