Quantum walk via open systems
J. P. Rodriguez · UWA Profiles and Research Repository (University of Western Australia) · 2016
In this thesis, we present a study of quantum walks with an open quantum system formalism. In this way we allow the walkers to interact with a surrounding environment, and by doing so we are able to add directionality to the paths that the walkers take on a given graph. A theoretical and mathematical framework for performing a directed quantum walk is established, which works for general continuous-time quantum walks on any weighted and/or directed graphs. Since quantum correlations, such as entanglement and quantum discord, play an important role in quantum computation and quantum information processing, a detailed study is also carried out on their dynamical change while two quantum particles walk through specified graphs. Finally the electron transport process in molecules is simulated using quantum walks, in particular in the Titanium dioxide (TiO2) electrode as well as the Fenna-Matthews-Olson protein complex. Quantum correlations are measured in these two systems, showing some evidence of entanglement assisted transport of the excitons in the Fenna-Matthews-Olson protein complex, but not in the TiO2 electrode.