A practical phase gate for producing Bell violations in Majorana wires

The Gottesman-Knill theorem holds that operations from the Clifford group, when combined with preparation and detection of qubit states in the computational basis, are insufficient for universal quantum computation. Indeed, any measurement results in such a system could be reproduced within a local hidden variable theory, so that there is no need for a quantum mechanical explanation and therefore no possibility of quantum speedup. Unfortunately, Clifford operations are precisely the ones available through braiding and measurement in systems supporting non-Abelian Majorana zero modes, which are otherwise an excellent candidate for topologically protected quantum computation. In order to move beyond the classically simulable subspace, an additional phase gate is required. This phase gate allows the system to violate the Bell-like CHSH inequality that would constrain a local hidden variable theory. In this article, we both demonstrate the procedure for measuring Bell violations in Majorana systems and introduce a new type of phase gate for the already existing semiconductor-based Majorana wire systems. We conclude with an experimentally feasible schematic combining the two, which should potentially lead to the demonstration of Bell violation in a Majorana experiment in the near future. Our work also naturally leads to a well-defined platform for universal fault-tolerant quantum computation using Majorana zero modes, which we describe.Comment: 11 pages, 13 figures; Title and references update

Topological minigap in quasi-one-dimensional spin-orbit-coupled semiconductor Majorana wires

The excitation gap above the Majorana fermion (MF) modes at the ends of 1D topological superconducting (TS) semiconductor wires scales with the bulk quasiparticle gap E_{qp}. This gap, also called minigap, facilitates experimental detection of the pristine TS state and MFs at experimentally accessible temperatures T << E_{qp}. Here we show that the linear scaling of minigap with E_{qp} can fail in quasi-1D wires with multiple confinement bands when the applied Zeeman field is greater than or equal to about half of the confinement-induced bandgap. TS states in such wires have an approximate chiral symmetry supporting multiple near zero energy modes at each end leading to a minigap which can effectively vanish. We show that the problem of small minigap in such wires can be resolved by forcing the system to break the approximate chirality symmetry externally with a second Zeeman field. Although experimental signatures such as zero bias peak from the wire ends is suppressed by the second Zeeman field above a critical value, such a field is required in some important parameter regimes of quasi-1D wires to isolate the topological physics of end state MFs. We also discuss the crucial difference of our minigap calculations from the previously reported minigap results appropriate for idealized spinless p-wave superconductors and explain why the clustering of fermionic subgap states around the zero energy Majorana end state with increasing chemical potential seen in the latter system does not apply to the experimental TS states in spin-orbit coupled nanowires.Comment: Crucial difference of the present results with previously reported results for idealized spinless p-wave wires discussed (see conclusion); new references added; Title changed in response to Editor comment; new version as accepted in PR

How to realize a robust practical Majorana chain in a quantum dot-superconductor linear array

Semiconducting nanowires in proximity to superconductors are promising experimental systems for Majorana fermions, which may ultimately be used as building blocks for topological quantum computers. A serious challenge in the experimental realization of the Majorana fermions is the supression of topological superconductivity by disorder. We show that Majorana fermions protected by a robust topological gap can occur at the ends of a chain of quantum dots connected by s-wave superconductors. In the appropriate parameter regime, we establish that the quantum dot/superconductor system is equivalent to a 1D Kitaev chain, which can be tuned to be in a robust topological phase with Majorana end modes even in the case where the quantum dots and superconductors are both strongly disordered. Such a spin-orbit coupled quantum dot - s-wave superconductor array provides an ideal experimental platform for the observation of non-Abelian Majorana modes.Comment: 8 pages; 3 figures; version 2: Supplementary material updated to include more general proof for localized Majorana fermion

Probing a topological quantum critical point in semiconductor-superconductor heterostructures

Quantum ground states on the non-trivial side of a topological quantum critical point (TQCP) have unique properties that make them attractive candidates for quantum information applications. A recent example is provided by s-wave superconductivity on a semiconductor platform, which is tuned through a TQCP to a topological superconducting (TS) state by an external Zeeman field. Despite many attractive features of TS states, TQCPs themselves do not break any symmetries, making it impossible to distinguish the TS state from a regular superconductor in conventional bulk measurements. Here we show that for the semiconductor TQCP this problem can be overcome by tracking suitable bulk transport properties across the topological quantum critical regime itself. The universal low-energy effective theory and the scaling form of the relevant susceptibilities also provide a useful theoretical framework in which to understand the topological transitions in semiconductor heterostructures. Based on our theory, specific bulk measurements are proposed here in order to characterize the novel TQCP in semiconductor heterostructures.Comment: 8+ pages, 5 figures, Revised version as accepted in PR

Predicción de la fenología de vicia faba l.: estimación de parámetros con el modelo cropgro- faba bean usando experimentos de múltiples fechas de siembra.

Entre los modelos de leguminosas más mecanicistas se puede destacar el modelo CROPGRO. Boote et al. (2002) adaptaron el CROPGRO para simular el crecimiento del haba (Vicia faba L.), naciendo así, CROPGRO-faba bean (incluido en el paquete DSSAT V4) en el que la tasa de desarrollo se expresa como día fisiológico (DF) transcurrido por día del calendario (día) (Ec. 1) y es una función multiplicativa de la temperatura (T) y fotoperíodo (P). Cada una de estas funciones adopta valores comprendidos entre 0 y

Predicting phenology of Vicia faba: Parameter estimation with CROPGRO-fababean model using multiple sowing date experiments.

Crop models have become valuable tools for designing efficient cropping systems, particularly once model reliability is documented for a given environment. For this use, the timing of crop phenology has to be accurately simulated to predict life cycle and the correct allocation of assimilates to yield components. The CROPGRO-Fababean model was developed based on adaptation of the generic CROPGRO legume model to simulate faba bean grown in Cordoba, Spain (Boote et al., 2002) but the model has not been tested extensively in other environments. Therefore, the model needs to be tested for additional environments, and may need to be modified to improve its reliability under a wide range of field conditions. For the initial model version, phase durations were calibrated against field data collected at Córdoba; however, the cardinal temperatures that affect phenology were derived from the literature. Because our goal was to use these parameters to make reliable predictions in new field environments, we propose that the best way to solve the coefficients is through a calibration process based on field data obtained under varying daily and seasonal temperature and daylength, similar to the method used successfully to calibrate the SOYGRO model phenology. The objective of this work was to determine quantitatively the effects of temperature and daylength on rate of vegetative node expression, time to flowering, time to beginning pod, time to beginning seed, and time to physiological maturity with the ultimate goal of making the CROPGRO-Faba bean model more reliable over a wide range of sowing date environments