Parker Kuklinski
My name is Parker Kuklinski and I am a recent PhD graduate from Boston University, where I wrote my thesis on "Absorption Phenomena in Quantum Walks". I am currently a Scientist at [redacted] where I research harmonic analysis problems in signal processing and topological quantum computing.
The quantum walk is a unitary analogue of the classical random walk. In two dimensions, the linearly expanding regions of polynomial decay of the probability distributions exhibit an intricate dependence on the governing unitary matrices. Inclusion of a greedy absorption unit causes slight decoherence which manifests as a smearing of the otherwise oscillatory interiors.
The quantum walks displayed are each governed by a canonical unitary matrix. The coloring reflects the proportion of probability in a given directional sub-state.