Achieving robust topological phases and qubit operations in the presence of long-range interactions

We theoretically explore 1D p-wave superconductors and dimerized chains in the presence of long-range couplings to achieve richer topological phases. We find that different regimes of long-range couplings yield non-trivial topological phases that inherit zero modes and massive edge modes. We find that long-range hopping in dimerized chains leads to multiple zero-modes whereas previously observed long-range pairing in p-wave superconductors gives rise to localized non-zero edge modes with fractional winding numbers. We characterize the topological origin of these phases using winding numbers and entanglement entropy. We further study the scope of quench dynamics of the entanglement spectrum as a signal to identify topological phase transitions in our models. Motivated by the above results, we extend our studies toward achieving robust single and multiqubit operations in our 1D models.