Executive Summary : | Quantum computers have the potential to efficiently simulate the dynamics of other quantum systems, but the ground-state preparation (GSP) problem is of great importance. This problem is particularly relevant for studying low-energy states, which contain information about interesting phases of matter like quantum Hall-effect, Bose-Einstein condensation, and superconductivity. An efficient quantum algorithm for the GSP problem would enable us to study these phenomena using a quantum computer. A wide range of optimization problems can be phrased as GSP problems, making the framework appealing even for near-term quantum devices. This proposal aims to make novel inroads to the problem of preparing ground states of Hamiltonians and provide new approaches to solving optimization problems using quantum computers. The first goal is to develop improved quantum algorithms for the ground-state preparation problem in both digital and analog models of quantum computation, providing a unified framework that encompasses all prior algorithms for this problem. The second goal is to address frameworks for solving optimization problems on near-term quantum computers, such as adiabatic quantum optimization (AQO), which encodes solutions of hard optimization problems. The project aims to quantify the speedup of AQO, a long-standing open problem, and explore the relationship between AQO and other frameworks expected to be implemented within the next few years. The research action is multidisciplinary and addresses cutting-edge problems in quantum algorithms. The proposal also includes plans for training and outreach. The outcomes of this proposal will significantly enhance the applicability of quantum computers for solving optimization problems, making it of significant interest to both academia and industry. |