Roadmap to Majorana surface codes

Surface codes offer a very promising avenue towards fault-tolerant quantum computation. We argue that two-dimensional interacting networks of Majorana bound states in topological superconductor/semiconductor heterostructures hold several distinct advantages in that direction, both concerning the hardware realization and the actual operation of the code. We here discuss how topologically protected logical qubits in this Majorana surface code architecture can be defined, initialized, manipulated, and read out. All physical ingredients needed to implement these operations are routinely used in topologically trivial quantum devices. In particular, we show that by means of quantum interference terms in linear conductance measurements, composite single-electron pumping protocols, and gate-tunable tunnel barriers, the full set of quantum gates required for universal quantum computation can be implemented.Comment: 23 pages, 8 figure

Towards realistic implementations of a Majorana surface code

Surface codes have emerged as promising candidates for quantum information processing. Building on the previous idea to realize the physical qubits of such systems in terms of Majorana bound states supported by topological semiconductor nanowires, we show that the basic code operations, namely projective stabilizer measurements and qubit manipulations, can be implemented by conventional tunnel conductance probes and charge pumping via single-electron transistors, respectively. The simplicity of the access scheme suggests that a functional code might be in close experimental reach.Comment: 5 pages, 1 p. suppl.mat, PRL in pres

Critical Workforce Skills for Bachelor-Level Geoscientists: An Analysis of Geoscience Job Advertisements

Understanding the skills bachelor-level geoscientists need to enter the workforce is critical to their success. The goal of this study was to identify the workforce skills that are most requested from a broad range of geoscience employers. We collected 3668 job advertisements for bachelor-level geoscientists and used a case-insensitive, code-matching function in Matlab to determine the skills geoscience employers seek. Written communication (67%), field skills (63%), planning (53%), and driving (51%) were most frequently requested. Field skills and data collection were frequently found together in the ads. Written communication skills were common regardless of occupation. Quantitative skills were requested less frequently (23%) but were usually mentioned several times in the ads that did request them, signaling their importance for certain jobs. Some geoscience-specific skills were rarely found, such as temporal understanding (5%) and systems thinking (0%). We also subdivided field skills into individual tasks and ranked them by employer demand. Site assessments and evaluations, unspecified field tasks, and monitoring were the most frequently requested field skills. This study presents the geoscience community with a picture of the skills sought by employers of bachelor-level geoscientists and provides departments and programs with data they can use to assess their curricula for workforce preparation

Diamagnetism of doped two-leg ladders and probing the nature of their commensurate phases

We study the magnetic orbital effect of a doped two-leg ladder in the presence of a magnetic field component perpendicular to the ladder plane. Combining both low-energy approach (bosonization) and numerical simulations (density-matrix renormalization group) on the strong coupling limit (t-J model), a rich phase diagram is established as a function of hole doping and magnetic flux. Above a critical flux, the spin gap is destroyed and a Luttinger liquid phase is stabilized. Above a second critical flux, a reentrance of the spin gap at high magnetic flux is found. Interestingly, the phase transitions are associated with a change of sign of the orbital susceptibility. Focusing on the small magnetic field regime, the spin-gapped superconducting phase is robust but immediately acquires algebraic transverse (i.e. along rungs) current correlations which are commensurate with the 4k_F density correlations. In addition, we have computed the zero-field orbital susceptibility for a large range of doping and interactions ratio J/t : we found strong anomalies at low J/t only in the vicinity of the commensurate fillings corresponding to delta = 1/4 and 1/2. Furthermore, the behavior of the orbital susceptibility reveals that the nature of these insulating phases is different: while for delta = 1/4 a 4k_F charge density wave is confirmed, the delta = 1/2 phase is shown to be a bond order wave.Comment: 15 pages, 17 figure

Current bistability and hysteresis in strongly correlated quantum wires

Nonequilibrium transport properties are determined exactly for an adiabatically connected single channel quantum wire containing one impurity. Employing the Luttinger liquid model with interaction parameter $g$, for very strong interactions g\lapx 0.2, and sufficiently low temperatures, we find an S-shaped current-voltage relation. The unstable branch with negative differential conductance gives rise to current oscillations and hysteretic effects. These non perturbative and non linear features appear only out of equilibrium.Comment: 4 pages, 1 figur

Spin-orbit coupling and electron spin resonance for interacting electrons in carbon nanotubes

We review the theoretical description of spin-orbit scattering and electron spin resonance in carbon nanotubes. Particular emphasis is laid on the effects of electron-electron interactions. The spin-orbit coupling is derived, and the resulting ESR spectrum is analyzed both using the effective low-energy field theory and numerical studies of finite-size Hubbard chains and two-leg Hubbard ladders. For single-wall tubes, the field theoretical description predicts a double peak spectrum linked to the existence of spin-charge separation. The numerical analysis basically confirms this picture, but also predicts additional features in finite-size samples.Comment: 19 pages, 4 figures, invited review article for special issue in J. Phys. Cond. Mat., published versio

Tomonaga-Luttinger liquid parameters of magnetic waveguides in graphene

Electronic waveguides in graphene formed by counterpropagating snake states in suitable inhomogeneous magnetic fields are shown to constitute a realization of a Tomonaga-Luttinger liquid. Due to the spatial separation of the right- and left-moving snake states, this non-Fermi liquid state induced by electron-electron interactions is essentially unaffected by disorder. We calculate the interaction parameters accounting for the absence of Galilei invariance in this system, and thereby demonstrate that non-Fermi liquid effects are significant and tunable in realistic geometries

Rashba spin-orbit coupling and spin precession in carbon nanotubes

The Rashba spin-orbit coupling in carbon nanotubes and its effect on spin-dependent transport properties are analyzed theoretically. We focus on clean non-interacting nanotubes with tunable number of subbands $N$. The peculiar band structure is shown to allow in principle for Datta-Das oscillatory behavior in the tunneling magnetoresistance as a function of gate voltage, despite the presence of multiple bands. We discuss the conditions for observing Datta-Das oscillations in carbon nanotubes.Comment: 12 pages, published versio