The 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. / Doctor of Philosophy / The computers we have now are able to perform computations by storing information in bits (units of memory which can take on either of two values e.g. 0 or 1) and then comparing and modifying the values of these bits according to a simple set of logical rules. The logic these computers use is suited to a universe that obeys the laws of classical mechanics, which was our best theory of physics prior to the 20th century, but the last 120 years have seen a radical shift in our understanding of nature. We now know that nature is much better described by the laws of quantum mechanics, which includes a great deal of surprising and unintuitive non-classical phenomena. The aim of quantum computing is to use our improved understanding of nature to design and build a new kind of computer which stores information in the states of quantum bits ("qubits") and then compares and modifies the combined state of these qubits using a logic adapted to the laws of quantum mechanics. By leveraging the quantum nature of reality, these quantum computers are capable of performing certain computations faster and more efficiently than is possible using classical computers.
The prospect of faster computing has inspired a massive effort to develop useful quantum computers, and the last forty years have seen impressive progress towards this goal, but there is a great deal left to do. Current quantum computing devices are too sensitive to their surroundings and far too error-prone to do useful computations. To reach tolerable error rates, we need to develop better devices and better methods for controlling those devices. Meanwhile, although several different device platforms are being continually developed, none of them currently operates with a collection of qubits anywhere near as large as the billions of bits our classical computers are able to use. It is not yet clear that practical scaling of these platforms up to that level is even possible, let alone how we can do so. Furthermore, only a handful of promising quantum algorithms have been discovered, and the efficiency of many is questionable at best. We have much that we still need to learn about what quantum computers can do and how best to use them.
This dissertation is a collection of seven papers arranged into three sections, all attempting to help address some of these issues. In the first two sections, we focus on one promising type of quantum computing platform -- solid-state electronic spin qubits. We introduce new methods for quickly performing quantum logic operations in these platforms, we suggest protocols for making these systems exhibit novel and potentially useful behavior, and we characterize and design control methods for a device design which might facilitate scaling up to large numbers of qubits. In the final section, we turn our attention to quantum software, and present two algorithms for using quantum computers to efficiently simulate physical systems at a fixed temperature.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/119419 |
| Date | 12 June 2024 |
| Creators | Warren, Ada Meghan |
| Contributors | Physics, Economou, Sophia Eleftherios, Nguyen, Vinh, Barnes, Edwin Fleming, Tauber, Uwe C. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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