Quantum circuit design for quantum walks
Oon Han Thomas Loke · UWA Profiles and Research Repository (UWA) · 2017
This thesis focuses on applying analytical and numerical techniques to the problem of designing quantum circuits for quantum walks. We develop efficient quantum circuit implementations of continuous-time quantum walks using diagonalization of the Hamiltonian. Next, for the discrete-time Szegedy quantum walk model, we provide a theoretical framework for the development of efficient quantum circuits, and apply it to a wide variety of graphs. We also investigate the optimisation of numerical techniques to the general problem of implementing a unitary matrix. Lastly, we discuss design principles for the development of efficient quantum circuit implementations of quantum walks of different types.