Adiabatic state preparation, which involves starting a quantum system in an easy-to-prepare ground state and slowly changing the Hamiltonian to a complex one while keeping the system in the ground state, is a powerful tool for preparing ground states of systems with complex Hamiltonians. By combining this method with the computational advantages of quantum computers, adiabatic state preparation has the potential to solve important quantum mechanical problems that cannot be solved with classical computing. However, for systems with ground states determined by different quantum numbers, conserved by symmetries of the Hamiltonian, adiabatic state preparation fails. This thesis demonstrates a generalization of adiabatic state preparation that overcomes this challenge by explicitly breaking the symmetry of the Hamiltonian. Here, the ground-state phase diagram of the one-dimensional two-site XY model, a ferromagnetic model for spin-1/2 particles, is calculated using this generalized procedure. The experimental results from quantum hardware are comparable with the exact solutions of the system. As quantum computing hardware becomes more robust, this procedure can be used to solve even larger systems and prepare even more ground-state phase diagrams.
- Code: The source code for the project is organized into code to run the circuit for 2 spin, 3 spin, and 4 spin systems.
- Positive and Negative Transitions: Positive and negative transitions contains the raw data and analysis results for each case.
- 3 Spin Result: Contains raw data for the 3 spin case.
- Images: Contains a zipped file of figures used in the thesis.