Our series of quantum mechanics related talks continues at full power. This week we have Stefan Boettcher (Emory) visiting us, and we have been discovering a lot of overlapping research lines! Stefan has a Science without Borders project with Renato Portugal, from the quantum information group at LNCC, and was very kind to drop by and deliver a talk here at CBPF. See the details of the talk below. See you there!
Speaker: Stefan Boettcher (Emory)
Coordinates: room 601D, CBPF. 14.08, 16:00h
Title: Renormalization Group for Quantum Walks
Abstract: Grover proposed a quantum algorithm to accomplish the search for an entry in an unstructured list that can succeed quadratically faster than any classical search algorithm. This has raised significant interest in designing theoretical and experimental implementations of such an algorithm in real, structured systems. There has been less focus on the physical engine that drives the quantum search, namely the quantum version of a random walk. Here, we analyze the asymptotic properties of such a quantum walk by developing the real-space renormalization group (RG), which we introduce for the simple walk on a line. Unitarity precludes the stochastic properties familiar from Markovian random walks. Thus, the canonical analysis of the RG-recursions at a real fixed-point is replaced by a study of chaotic attractors in the complex plane. In turn, we are rewarded with a rich phenomenology, such as localization effects, and some exact results.