Session D44: Invited Session: Topological Quantum Computing with Majorana Fermions

Non-abelian anyons and topological quantum information processing in 1D wire networks

Topological quantum computation provides an elegant solution to decoherence, circumventing this infamous problem at the hardware level. The most basic requirement in this approach is the ability to stabilize and manipulate particles exhibiting non-Abelian exchange statistics -- Majorana fermions being the simplest example. Curiously, Majorana fermions have been predicted to arise both in 2D systems, where non-Abelian statistics is well established, and in 1D, where exchange statistics of any type is ill-defined. An important question then arises: do Majorana fermions in 1D hold the same technological promise as their 2D counterparts? In this talk I will answer this question in the affirmative, describing how one can indeed manipulate and harness the non-Abelian statistics of Majoranas in a remarkably simple fashion using networks formed by quantum wires or topological insulator edges.   

Realization and detection of Majorana modes at generic spin-orbit coupled semiconductor/s-wave superconductor interfaces

Majorana fermions are hitherto unobserved particles that have been theoretically predicted to have non-Abelian statistics that may be used for Topological Quantum Computation. For over a decade the only candidate systems for observing Majorana fermions were the non-Abelian $\nu=5/2$ fractional quantum Hall state and chiral p-wave superconductors. More recently, motivated by developments in the area of topological insulators it was realized that a more general class of topological superconductors, some of which may be as simple as the interface of InAs and Al, should support such excitations. This talk will start by explaining why superconductors are a natural host for Majorana fermions. Following this, it will be argued that Majorana fermions should exist in generic semiconductor/superconductor interfaces, both in 1D and 2D, the crucial ingredients being s-wave superconductivity, spin-orbit coupling, and Zeeman splitting. Such Majorana fermions at the end of a nanowire appear as a magnetic-field tunable zero-bias peak in the STM spectrum with quantized conductance. Following this experimental challenges \textit{en route} to realizing Majorana fermions in these structures such as disorder and the required tuning of the chemical potential of the semiconductor, will be discussed. Finally, we will conclude by showing how the spin-orbit coupled nanowires motivate a class of intrinsically number conserving microscopic models for topological superconductor with end Majorana fermions. The bosonization approach used to study this one-dimensional model, directly connects the Majorana fermions, which are typically described as Bogoliubov quasiparticles in mean-field theory, to an emergent Ising order in the one-dimensional nanowire model. The robustness of the topological degeneracy to weak local perturbations can be explicitly demonstrated.   

The Search for Majorana Fermions in Semiconductor Nanowires

Majorana Fermions can arise as quasi-particles in specially designed nanoscale, electronic devices. Our approach is to use semiconductor nanowires with strong spin-orbit interaction (InAs or InSb). We induce superconductivity in the nanowires and control the electron density through a nearby gate. Several properties are measured such as the spin-orbit strength (including the dependence on the magnetic field direction), the induced superconducting gap (including magnetic field dependence) and the flow of supercurrents. For the determined experimental values we estimate the temperature scale to be $\sim $2 Kelvin as the transition temperature for the reaching the phase of a topological superconductor. Majorana Fermions should be detectable as special features in the tunneling conductance or in the periodicity of an interferometer setup (SQUID geometry).   

Manipulation of Majorana fermions using superconducting qubits

Majorana fermions are special particles, predicted to appear in certain superconductors. They are extremely useful for quantum computation, due to the possibility to store quantum information in the degenerate ground state of the system. Moreover braiding Majorana fermions around each other allows to implement certain quantum gates in a fault-tolerant manner. I introduce a scheme of quantum computation with Majorana fermions which relies on interplay of charging and Josephson energy to measure, controllably couple, and braid Majorana fermions. The advantage of this scheme is that it fully relies on control elements usual for superconducting cirquitry and does not require fine tuning on the scale of Fermi wavelength.   

Disorder effects in topological quantum wires, and alternative platforms for Majorana Fermion realization

Spinless p-wave superconducting wires can be in a topological phase in which they harbor Majorana bound states at their ends. Although there are no known spinless p-wave superconductors in nature, several routes to the artificial creation of such systems have been proposed. In this talk, I will discuss how non-idealities in some of the proposed routes, such as potential disorder and deviations from a strict one-dimensional limit, affect the topological phase. In particular, I'll discuss how the topological phase can persist at weak disorder or for multichannel wires, although some of the signatures of the presence of Majorana fermions are obscured.