Charge response of the Majorana toric code

At zero temperature, a two dimensional lattice of Majorana zero modes on mesoscopic superconducting islands has a topologically ordered toric code phase. Recently, a Landau field theory has been proposed for the system that captures its different phases and the associated phase-transitions. It was shown that with the increase of Josephson tunneling between the islands, a continuous symmetry-breaking 3D-XY transition gets transformed into a discrete symmetry-breaking 3D-Ising transition through a couple of tricritical points and first order transitions. Using the proposed field theory, we analyze the charge-response of the system at the different continuous phase-transitions. We calculate the universal conductivity at the 3D-XY transitions and the change in the superconducting density at the Ising transition using 1/N expansion. Furthermore, by computing a one-loop correction to the field theory, we show that an additional tricritical point is likely to be present in the phase-diagram. Finally, we provide a mean-field calculation that supports the earlier proposed field theory.Comment: Published versio

Quantum phase transitions of the Majorana toric code in the presence of finite Cooper-pair tunneling

The toric code based on Majorana fermions on mesoscopic superconducting islands is a promising candidate for quantum information processing. In the limit of vanishing Cooper-pair tunneling, it has been argued that the phase transition separating the topologically ordered phase of the toric code from the trivial one is in the universality class of (2+1)D-XY. On the other hand, in the limit of infinitely large Cooper-pair tunneling, the phase transition is in the universality class of (2+1)D-Ising. In this work, we treat the case of finite Cooper-pair tunneling and address the question of how the continuous XY symmetry breaking phase transition turns into a discrete $\mathbb{Z}_2$ symmetry breaking one when the Cooper-pair tunneling rate is increased. We show that this happens through a couple of tricritical points and first order phase transitions. Using a Jordan-Wigner transformation, we map the problem to that of spins coupled to quantum rotors and subsequently, propose a Landau field theory for this model that matches the known results in the respective limits. We calculate the effective field theories and provide the relevant critical exponents for the different phase transitions. Our results are relevant for predicting the stability of the topological phase in realistic experimental implementations.Comment: 5 pages, 2 figure

Mapping constrained optimization problems to quantum annealing with application to fault diagnosis

Current quantum annealing (QA) hardware suffers from practical limitations such as finite temperature, sparse connectivity, small qubit numbers, and control error. We propose new algorithms for mapping boolean constraint satisfaction problems (CSPs) onto QA hardware mitigating these limitations. In particular we develop a new embedding algorithm for mapping a CSP onto a hardware Ising model with a fixed sparse set of interactions, and propose two new decomposition algorithms for solving problems too large to map directly into hardware. The mapping technique is locally-structured, as hardware compatible Ising models are generated for each problem constraint, and variables appearing in different constraints are chained together using ferromagnetic couplings. In contrast, global embedding techniques generate a hardware independent Ising model for all the constraints, and then use a minor-embedding algorithm to generate a hardware compatible Ising model. We give an example of a class of CSPs for which the scaling performance of D-Wave's QA hardware using the local mapping technique is significantly better than global embedding. We validate the approach by applying D-Wave's hardware to circuit-based fault-diagnosis. For circuits that embed directly, we find that the hardware is typically able to find all solutions from a min-fault diagnosis set of size N using 1000N samples, using an annealing rate that is 25 times faster than a leading SAT-based sampling method. Further, we apply decomposition algorithms to find min-cardinality faults for circuits that are up to 5 times larger than can be solved directly on current hardware.Comment: 22 pages, 4 figure

Dual Shapiro steps of a phase-slip junction in the presence of a parasitic capacitance

Bloch oscillations in a single Josephson junction in the phase-slip regime relate current to frequency. They can be measured by applying a periodic drive to a DC-biased, small Josephson junction. Phase-locking between the periodic drive and the Bloch oscillations then gives rise to steps at constant current in the I-V curves, also known as dual Shapiro steps. Unlike conventional Shapiro steps, a measurement of these dual Shapiro steps is impeded by the presence of a parasitic capacitance. This capacitance shunts the junction resulting in a suppression of the amplitude of the Bloch oscillations. This detrimental effect of the parasitic capacitance can be remedied by an on-chip superinductance. Additionally, we introduce a large off-chip resistance to provide the necessary dissipation. We investigate the resulting system by a set of analytical and numerical methods. In particular, we obtain an explicit analytical expression for the height of dual Shapiro steps as a function of the ratio of the parasitic capacitance to the superinductance. Using this result, we provide a quantitative estimate of the dual Shapiro step height. Our calculations reveal that even in the presence of a parasitic capacitance, it should be possible to observe Bloch oscillations with realistic experimental parameters.Comment: 5+3 pages; 3 figure

Control interno y su incidencia en la productividad al área de servicio en una empresa privada - 2020

El presente trabajo de investigación muestra el “Control Interno en la productividad del Área de servicio en una empresa privada - 2020”, que tiene como objetivo determinar la contribución del Control Interno en la productividad del estudio contable. De esta manera el Control Interno guarda una relación importante con la gestión que desarrollo la compañía, en este caso se determinó cómo esta herramienta influyo en la productividad de la organización y como beneficio a la empresa para el cumplimiento de sus objetivos, esto mismo incentivo a que se identificaran los riesgos para cuidar de los activos que tiene la empresa seleccionando y desarrollando todos los controles para mitigar los riesgos que afecten el normal funcionamiento de sus operaciones. Para que lo expuesto en el párrafo anterior se haya llevado a cabo se aplicó el sistema de Control Interno (SCI) y todos sus componentes interrelacionados según el modelo COSO 2017, el cual está enfocado en mejorar todos los procesos que no están siendo desarrollados de manera adecuada por el estudio contable, de esta manera, con la aplicación del Control Interno buscamos aumentar el nivel de productividad de dicha organización.The present research work shows the “Internal Control in the productivity of the Service Area in a private company - 2020”, which aims to determine the contribution of Internal Control in the productivity of the accounting study. In this way, Internal Control has an important relationship with the management that the company developed, in this case it was determined how this tool influenced the productivity of the organization and as a benefit to the company for the fulfillment of its objectives, this same incentive to That the risks to take care of the assets that the company has will be identified, selecting and developing all the controls to mitigate the risks that affect the normal functioning of its operations. For the in the previous paragraph to be carried out, the Internal Control system (ICS) and all its interrelated components were applied according to the COSO 2017 model, which is focused on improving all the processes that are not being developed in such a way. adequate for the accounting study, in this way, with the application of Internal Control we seek to increase the level of productivity of said organization

Monitoring On-line Timing Information to Support Mixed-Critical Workloads

International audienceMany/multi-cores architectures provide tremendous increase in computation power, increasing the possibility of executing additional tasks on the system. In critical embedded systems, e.g. aeronautical systems, the uncertainty of the non-uniform and concurrent memory access scheme prohibits the full utilization of the system potentials. Classical Worst Case Execution Time (WCET) estimation techniques upper bound the memory accesses -considering a fully congested memory bus - resulting in safe, but pessimistic, bounds. The proposed approach explores the increase in the system utilization by less critical tasks, while guaranteeing the safety of the critical task

Publisher’s Note: “Polymer drag reduction in exact coherent structures of plane shear flow” [Phys. Fluids 16, 3470 (2004)]

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69804/2/PHFLE6-16-12-4761-1.pd

Transformer Utilization in Medical Image Segmentation Networks

Owing to success in the data-rich domain of natural images, Transformers have recently become popular in medical image segmentation. However, the pairing of Transformers with convolutional blocks in varying architectural permutations leaves their relative effectiveness to open interpretation. We introduce Transformer Ablations that replace the Transformer blocks with plain linear operators to quantify this effectiveness. With experiments on 8 models on 2 medical image segmentation tasks, we explore -- 1) the replaceable nature of Transformer-learnt representations, 2) Transformer capacity alone cannot prevent representational replaceability and works in tandem with effective design, 3) The mere existence of explicit feature hierarchies in transformer blocks is more beneficial than accompanying self-attention modules, 4) Major spatial downsampling before Transformer modules should be used with caution.Comment: Accepted in NeurIPS 2022 workshop, Medical Imaging Meets NeurIPS (MedNeurIPS