5 research outputs found
Topological Insulators in the Honeycomb Lattice
We investigate realizations of topological insulators with spin-1 bosons
loaded in a honeycomb optical lattice and subjected to a spin-orbit
coupling - a situation which can be realized experimentally using cold atomic
gases. In this paper, we focus on the topological properties of the
single-particle band structure, namely Chern numbers (lattice with periodic
boundary conditions) and edge states (lattice with strip geometry). While
spin-orbit couplings always lead to time-reversal symmetric Hubbard
models, and thereby to topologically trivial band structures, suitable
spin-orbit couplings can break time reversal symmetry and lead to topologically
non-trivial bulk band structures and to edge states in the strip geometry. In
addition, we show that one can trigger a series of topological transitions
(i.e. integer changes of the Chern numbers) that are specific to the geometry
of the honeycomb lattice by varying a single parameter in the Hamiltonian.Comment: 12 pages, 8 figure
Multi-Objective Optimization and Network Routing with Near-Term Quantum Computers
Multi-objective optimization is a ubiquitous problem that arises naturally in
many scientific and industrial areas. Network routing optimization with
multi-objective performance demands falls into this problem class, and finding
good quality solutions at large scales is generally challenging. In this work,
we develop a scheme with which near-term quantum computers can be applied to
solve multi-objective combinatorial optimization problems. We study the
application of this scheme to the network routing problem in detail, by first
mapping it to the multi-objective shortest path problem. Focusing on an
implementation based on the quantum approximate optimization algorithm (QAOA)
-- the go-to approach for tackling optimization problems on near-term quantum
computers -- we examine the Pareto plot that results from the scheme, and
qualitatively analyze its ability to produce Pareto-optimal solutions. We
further provide theoretical and numerical scaling analyses of the resource
requirements and performance of QAOA, and identify key challenges associated
with this approach. Finally, through Amazon Braket we execute small-scale
implementations of our scheme on the IonQ Harmony 11-qubit quantum computer
TOPOLOGICAL PROPERTIES OF THE SPIN-1 BOSE GAS IN THE HONEYCOMB LATTICE
Ph.DDOCTOR OF PHILOSOPHY (CQT
Non-equilibrium expansion dynamics of strongly correlated bosons in a 2d optical lattice
In this thesis we discussed the expansion behaviour of an ultracold bosonic gas from an initial harmonic confinement. We studied the reaction of the non-interacting system to changes of the trap frequency ω and of the strongly interacting system to changes of the number of Mott insulating particles NMI in the initial state and the interaction U/J. The total number of particles is kept constant for the different simulations, which are performed by means of the Bosonic Gutzwiller approach..