Topological order detection and qubit encoding in Su-Schrieffer-Heeger type quantum dot arrays

Abstract

In this study, building on the 1D topological Su-Schrieffer-Heeger (SSH) model, we propose a model of quantum dot arrays with odd and even parity and variable on-site local potentials to examine topological edge states and a possible quantum information encoding, using these states. We first investigate the SSH model with alternating tunneling amplitudes t 1 and t 2. We study the model in a ring-like structure and then proceed to minimal open-end chains with even (N = 4) and odd (N = 5) number of dots. Furthermore, we depart from the basic SSH model by introducing local potentials μ i, which offer additional control at the cost of breaking the chiral symmetry of the Hamiltonian and study the implications. Then, we propose an idealized "static"charge qubit design, based on encoding the topological invariant ν as qubit states, that exploits the topological nature of the edge states and their collective character. We introduce perturbing noise δ t i j (t) into the system and demonstrate the robustness of the states for some range of the ratio ζ = t 1 / t 2. Moreover, we show a possible way to detect the presence of topological order in the system using equilibrium dynamics for both even and odd chains. We utilize the quantum informatic measure of bipartite mutual information I { b: e } (2) (t) as a measure of bulk-edge quantum correlations and a quantitative indicator for the manifestation of bulk-edge correspondence; here, we also propose a dynamical qubit encoding with ν for specific quantum chain parity. Finally, we offer a few remarks on potential future explorations.