Scalable Gate-Defined Majorana Fermions in 2D p-Wave Superconductors

Abstract: We provide a conceptual framework for developing a scalable topological quantum computer. It relies on forming Majorana fermions using circular electronic gates in two-dimensional p-wave superconductors. The gates allow the precise control of the number, position, and dynamics of Majorana fermions. Using an array of such gates, one can implement the full features of topological quantum computation, including the braiding and fusion of Majoranas in space-time. The gates serve two purposes: They modulate the chemical potential locally to turn a topological superconductor into a normal conductor, and they are used to move the Majoranas in space-time. With a perpendicular magnetic field, the normal region localizes a quantum of magnetic flux. Under these conditions, the boundary between the normal region and the superconducting region supports a single zero-energy Majorana bound state. The localized zero mode is sufficiently separate from other states and can be dragged by sequentially applying voltages to the adjacent gates to implement quantum computation. We briefly describe the fabrication process to construct the device and determine key properties from experimentally determined parameters. The digital qualities of topological protection provide intrinsic immunity to the inevitable fabrication nonuniformities.