Localization of space-inhomogeneous three-state quantum walks

Localization and fractality in inhomogeneous quantum walks with self-duality.

We introduce and study a class of discrete-time quantum walks on a one-dimensional lattice. In contrast to the standard homogeneous quantum walks, coin operators are inhomogeneous and depend on their positions in this class of models. The models are shown to be self-dual with respect to the Fourier transform, which is analogous to the Aubry-André model describing the one-dimensional tight-bindi...

Localization in an inhomogeneous quantum wire

We study interaction-induced localization of electrons in an inhomogeneous quasi-one-dimensional system—a wire with two regions, one at low density and the other high. Quantum Monte Carlo techniques are used to treat the strong Coulomb interactions in the low-density region, where localization of electrons occurs. The nature of the transition from high to low density depends on the density grad...

Disorder, Localization and Decay in Quantum Walks

Quantum Walks and Ground State Problems

OF THE DISSERTATION Quantum walks and ground state problems by Peter Courtland Richter Dissertation Director: Mario Szegedy Since the appearance of Shor’s factoring algorithm in 1994, the search for novel quantum computer algorithms has proved surprisingly difficult. Two design approaches that have yielded some progress are quantum walks and adiabatic computing. The former has been shown to spe...

Coin state properties in quantum walks

Recent experimental advances have measured individual coin components in discrete time quantum walks, which have not received the due attention in most theoretical studies on the theme. Here is presented a detailed investigation of the properties of M, the difference between square modulus of coin states of discrete quantum walks on a linear chain. Local expectation values are obtained in terms...