Topological quantum computing - the poor man's Majorana

Abstract

In this report, we establish the groundwork for the emergence of Majoranas - particles that are their own anti-particles - in superconducting systems. We observe that such Majoranas manifest as edge states, and when they are sufficiently separated and coupled, they offer topological protection due to the non-locality of these states. Following this, we discuss a realistic system in which Majorana bound states could exist, including the conditions necessary for such a system. We examine the effects of each term in the realistic system's Hamiltonian. Additionally, we have performed conductance simulations to confirm the presence of Majorana bound state signatures and adapted this system to realistic experimental parameters. Our results demonstrate that an ideal 100 nm semiconductor-superconductor Kitaev chain can achieve topological protection on the order of 10e-5. We also explore perturbations, specifically those induced by temperature, and find that recent experiments likely maintain sufficiently topologically protected Majorana bound states, if not for device impurities and non-topological states.