Practical design and demonstration of algorithms for quantum devices

Abstract

The emergence of noisy intermediate-scale quantum (NISQ) devices represents a significant milestone in the journey towards the development of large-scale fault tolerant quantum computers. These devices have not only opened avenues for demonstrating a quantum advantage but have also advanced the practical development of quantum algorithms for solving challenging problems in physics, chemistry, and computer science. Most notably, this progress has necessitated a tailored approach to algorithm development that considers the specific architecture and hardware constraints of these quantum devices in order to effectively use them. However, the most useful instances of problems that we hope to solve with quantum computers require significant hardware improvements over the state-of-the-art, including at least a hundred fold increase in the number of qubits. The transition from intermediate-scale to large-scale quantum computers also presents other formidable challenges, particularly for engineering precise quantum control at scale. This thesis attempts to narrow the gap between intermediate and large-scale devices by proposing methods to mitigate noise effects on NISQ devices and by enhancing standard quantum algorithms to minimize resource overhead. One focus is on error correction strategies capable of managing noise on quantum devices. Specifically, we demonstrate the robustness of the sweep rule (a decoder for topological quantum codes) against measurement errors in quantum codes. Additionally, we experimentally demonstrate the improvement in performance of entangling non-Clifford operations when encoded in the [[8,3,2]] code, strengthening the case for error correction. Furthermore, we improve a well-known technique known as imaginary time evolution to reduce the associated qubit and entangling gate overhead, making it more amenable to implementation on NISQ devices. By exploring these avenues, we aim to strike a balance, leveraging NISQ devices to expand their computational capabilities in the short term while serving as a sandbox for the development of future large-scale fault-tolerant quantum computers.