The quest to design a realizable quantum computer is a dream for many for the past few decades. At the moment, one of the promising designs is the transmon qubit, which is a superconducting qubit is the focus of this work. In order to analyze and design different components of a quantum chip, an understanding of the circuitry is required. By varying the circuit parameters, one can design the system according to requirements by constructing the required physical geometry that incorporates the design parameters. In this thesis work, part of the focus was to understand the transmon qubit circuit parameters, extract the circuit parameters such as capacitances from a physical geometry, build analytic and numerical 3D FEM models. Using a circuit model of the qubit system, the interdependence of the resonators that connects qubits with each other can be studied. Their resonances play a role in the qubit Hamiltonian and can be estimated by constructing accurate simulation models. This problem statement has been dealt with in the thesis work by constructing a hybrid circuitry of standard circuit components and 3D FEM simulated qubit unit cells. The quality factor of the measurement readout resonator of a qubit system needs to be characterized in a qubit system in order to target the rate and resolution at which the measurements can be done. In order to do so, the circuit parameters that affect the quality factor needs to be investigated. This problem statement has also been treated in this work.

For microwave qubit readout in research applications, a Vector Network Analyser has been designed. The objective of this project was to design and build a modular, extensible VNA, containing open hard- ware and implemented in open-source software. This thesis discusses the Python implementation of an interface between the digital signal processing step, taking place inside an FPGA, and the output of data to the user, being in graphical form and as systematical data structure to be stored on a PC. The interface is split up into a server, responsible for communicating with the FPGA on the same chip, and a client, which receives the measurement data from the server via the Transmission Control Protocol and controls the radio frequency signal genera- tors that serve as stimulus for the device under test and as local oscillator for downconversion. An overview of VNAs and their application in this project is given in the first chapter. The programme of requirements and implementation overview are discussed next, followed by detailed explanations of the Python implementation of the server and client software. The achieved results satisfy the requirements for throughput, extensibility and data transfer overhead time. The thesis concludes with recommendations for future developments and extensions to this project.

This thesis presents the design, implementation, and evaluation of the RF (Radio Frequency) section of an Open-Hardware Vector Network Analyzer (VNA) intended for quantum research applications. The project aims to create a cost-effective, modular VNA system that fulfills the functional requirements necessary for qubit readout and other quantum measurements. In the initial chapters, the overall architecture of the VNA is outlined, with specific attention to the power budget and system requirements. The RF generation principles are examined, and a range of RF generators are tested to ensure they meet the signal quality standards, such as spurious emissions and harmonic content. The performance of various RF mixers is also evaluated and found to be sufficient for the RF system. Experimental results demonstrate the system’s capability to measure the S21 parameter of a resonator cavity, comparable to commercial VNAs. This validates that the RF system meets the specified requirements and can be effectively used in quantum research. Future work suggested includes the measurement of generator frequency/phase stability over time and exploring the feasibility of implementing power sweeps to enhance the system’s functionality. The findings of this thesis contribute to the development of accessible and flexible tools for quantum technology research, promoting further advancements in the field.

This thesis discusses the digital signal processing involved in building a Vector Network Analyser for qubit readout. Existing VNAs are aggregated and used to construct a programme of requirements for this application. An architecture is constructed and explained, and the stages IQ decomposition and data reduction are analysed mathematically. The Discrete Fourier Transform is used to extract DC signals for this application and its properties are compared to different filters. Common digital logic functions such as AXI, Direct Digital Synthesis, and Direct Memory Access are explained, as well as the implementations of custom blocks for this application such as accumulators and a sequencer. These IP blocks are demonstrated individually and integrated to be implemented on a Red Pitaya STEMLab 125-14 board containing the Zynq 7010 SoC. The implementation is tested using simulated input signals and the resulting measurements are analysed. The implementation is found to have good absolute accuracy of within 2% of expected absolute amplitude, 1% of the expected relative amplitude and 8 mrad of expected relative phase. Modulation of the input signals is tested to work as expected and no major cross-modulation is found. Future improvements are identified and the limitations of the used data reduction are discussed in relation to a Vector Signal Analyser mode.