Warren, Ada Meghan2024-06-132024-06-132024-06-12vt_gsexam:41083https://hdl.handle.net/10919/119419The last forty years have seen an astounding level of progress in the field of quantum computing. Rapidly-improving techniques for fabricating and controlling devices, increasingly refined theoretical models, and innovative quantum computing algorithms have allowed us to pass a number of important milestones on the path towards fault-tolerant general purpose quantum computing. There remains, however, uncertainty regarding the feasibility and logistics of scaling quantum computing platforms to useful sizes. A great deal of work remains to be done in developing sophisticated control techniques, designing scalable quantum information processing architectures, and creating resource-efficient algorithms. This dissertation is a collection of seven manuscripts organized into three sections which aim to contribute to these efforts. In the first section, we explore quantum control techniques for exchange-coupled solid-state electronic spin qubits in arrays of gate-defined quantum dots. We start by demonstrating theoretically the existence of a discrete time crystal phase in finite Heisenberg spin chains. We present driving pulses that can be used to induce time crystalline behavior and probe the conditions under which this behavior can exist, finding that it should be realizable with current experimental capabilities. Next, we use a correspondence between quantum time evolution geometric space curves to design fast, high-fidelity entangling gates in two-spin double quantum dots. In the second section, we study systems of quantum dot spin qubits coupled to one another via mutual coupling to superconducting microwave resonators. We start with two qubits, developing and refining an effective model of resonator-mediated entangling interactions, and then use that model to ultimately design fast, long-distance, high-fidelity entangling gates which are robust to environmental noise. We then take the model further, extending our model to a system of three qubits coupled by a combination of short-range exchange interactions and long-range resonator-mediated interactions, and numerically demonstrate that previously-developed protocols can be used to realize both short- and long-range entangling operations. The final section investigates adaptive variational algorithms for efficient preparation of thermal Gibbs states on a quantum computer, a difficult task with a number of important applications. We suggest a novel objective function which can be used for variational Gibbs state preparation, but which requires fewer resources to measure than the often-used Gibbs free energy. We then introduce and characterize two variational algorithms using this objective function which adaptively construct variational ansätze for Gibbs state preparation.ETDenIn CopyrightQuantum computingQuantum controlElectronic spin qubitsVariational quantum algorithmsDissertation