Quantum Dynamical Characterization and Simulation of Topological Phases With High-Order Band Inversion Surfaces

Topological phases and quantum computation

Exploring topological phases with quantum walks

The quantum walk was originally proposed as a quantum-mechanical analog of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete-time quantum walks provide a versatile platform for studying topological phases, which are currently the subject of intense theoretical and experimental investigations. In particular, we de...

Topological Phases in Narrow-band syst(

I discuss several novel topological phases in correlated electron systems, realized through spin-orbit interactions and lattice effects especially narrow-band systems. The first realizes the fractional quantum Hall effect using geometric frustration and ferromagnetism to obtain a nearly flat band with a large bandgap and non-zero Chern number. This system can support this effect at high tempera...

Topological Nonsymmorphic Metals from Band Inversion

Lukas Muechler, A. Alexandradinata, Titus Neupert, and Roberto Car Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA Department of Physics, Yale University, New Haven, Connecticut 06520, USA Department of Physics, Princeton University, Princeton, New Jersey 08544, USA Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA a...

Geometric Phases and Topological Quantum Computation

In the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also introduce a number of examples that will help the reader understand the basic issues involved. In the second part we show how to perform a universal quantum comp...