Quantum computing has seen remarkable progress over the past decade, with superconducting qubits emerging as one of the leading hardware platforms for its physical realisation. Among the various superconducting qubit architectures, the transmon has been one of the most widely adopted candidates, owing to its relatively simple design and compatibility. However, the transmon suffers from key limitations, most notably its weak anharmonicity and multi-qubit gates using transmon being difficult to execute faster without errors.
In this context, alternative qubit architectures have attracted interest. The fluxonium qubit, with its large anharmonicity and long coherence times, has emerged as a promising candidate for overcoming shortcomings of the transmon. Similarly, the cos(2φ) qubit offers an intriguing design with inherent noise protection, making it a compelling subject of investigation for next-generation superconducting hardware.
Beyond the question of which qubit to build, a central challenge in quantum computing is the realisation of high-fidelity two-qubit gates. Higher gate fidelity directly translates to better quantum operations and is essential for the implementation of error correction protocols. Equally important is the question of how to perform these gates in a fast and practical manner—ideally using simple pulse techniques that minimise the time and effort required for calibration.
This thesis addresses these themes across two broad directions. First, we explore the fabrication of fluxonium and cos(2φ) qubits, developing improved processes and cleanroom techniques to achieve more reliable and reproducible devices. Second, we investigate two-qubit gate operations using analytic pulse techniques, with the goal of realising faster and simpler gates that reduce the overhead associated with pulse calibration. Together, these contributions advance the development of superconducting qubit platforms towards more practical and scalable quantum computing.

Two-qubit gates constitute fundamental building blocks in the realization of large-scale quantum devices. Using superconducting circuits, two-qubit gates have been implemented in various ways, with each method aiming to maximize gate fidelity. Another important goal of a new gate scheme is to minimize the complexity of gate calibration. In this work, we demonstrate a high-fidelity two-qubit gate between two fluxonium qubits, enabled by an intermediate capacitively coupled transmon. The coupling strengths between the qubits and the coupler are designed to minimize residual crosstalk while still allowing for fast gate operations. The gate is based on frequency selectively exciting the coupler using a microwave drive to complete a 2π rotation, conditional on the state of the fluxonium qubits. When successful, this drive scheme implements a conditional phase gate. Using analytically derived pulse shapes, we minimize unwanted excitations of the coupler and obtain gate errors of 10−2 for gate times below 60 ns. At longer durations, the gate performance is limited by relaxation of the coupler. Our results show how carefully designed control pulses can speed up frequency-selective entangling gates.

Superconducting circuits are being used for large-scale quantum devices, and a major challenge is to perform accurate numerical simulations of device parameters. One of the most advanced methods for analyzing superconducting circuit designs is the energy-participation-ratio (EPR) method, which constructs quantum Hamiltonians based on the energy distribution extracted from classical electromagnetic simulations. In the EPR approach, we extract linear terms from finite-element simulations and add nonlinear terms using the energy participation ratio extracted from the classical simulations. However, the EPR method relies on a low-order expansion of nonlinear terms, which is prohibitive for accurately describing highly anharmonic circuits. An example of such a circuit is the fluxonium qubit, which has recently attracted increasing attention due to its high lifetimes and low error rates. In this work, we extend the EPR approach to effectively address highly nonlinear superconducting circuits, and, as a proof of concept, we apply our approach to a fluxonium qubit. Specifically, we design, fabricate, and experimentally measure a fluxonium qubit coupled to a readout resonator. We compare the measured frequencies of both the qubit and the resonator to those extracted from the EPR analysis, and we find an excellent agreement. Furthermore, we compare the dispersive shift as a function of external flux obtained from experiments with our EPR analysis and a simpler lumped-element model. Our findings reveal that the EPR results closely align with the experimental data, providing more accurate estimations compared to the simplified lumped-element simulations.

In many quantum platforms, single-qubit gates are applied using a linear drive resonant with the qubit transition frequency, which is often theoretically described within the rotating-wave approximation (RWA). However, for fast gates on low-frequency qubits, the RWA may not hold and we need to consider the contribution from counterrotating terms to the qubit dynamics. The inclusion of counterrotating terms into the theoretical description gives rise to two challenges. First, it becomes challenging to analytically calculate the time evolution as the Hamiltonian is no longer self-commuting. Moreover, the time evolution now depends on the carrier phase such that, in general, every operation in a sequence of gates is different. In this work, we derive and verify a correction to the drive pulses that minimizes the effect of these counterrotating terms in a two-level system. We then derive a second correction term that arises from noncomputational levels for a strongly anharmonic system. We experimentally implement these correction terms on a fluxonium superconducting qubit, which is an example of a strongly anharmonic, low-frequency qubit for which the RWA may not hold, and demonstrate how fast, high-fidelity single-qubit gates can be achieved without the need for additional hardware and calibration complexities.