Recurrent neural network decoding of rotated surface codes based on distributed strategy

Quantum error correction is a crucial technology for realizing quantum computers.These computers achieve faulttolerant quantum computing by detecting and correcting errors using decoding algorithms.Quantum error correction using neural network-based machine learning methods is a promising approach that is adapted to physical systems without the need to build noise models.In this paper,we use a distributed decoding strategy,which effectively alleviates the problem of exponential growth of the training set required for neural networks as the code distance of quantum error-correcting codes increases.Our decoding algorithm is based on renormalization group decoding and recurrent neural network decoder.The recurrent neural network is trained through the ResNet architecture to improve its decoding accuracy.Then we test the decoding performance of our distributed strategy decoder,recurrent neural network decoder,and the classic minimum weight perfect matching(MWPM)decoder for rotated surface codes with different code distances under the circuit noise model,the thresholds of these three decoders are about 0.0052,0.0051,and 0.0049,respectively.Our results demonstrate that the distributed strategy decoder outperforms the other two decoders,achieving approximately a 5%improvement in decoding efficiency compared to the MWPM decoder and approximately a 2%improvement compared to the recurrent neural network decoder.

RotateTransform函数在船舶仪表控件编写中的运用及数学分析

应用最新的GDI+和Visual C#.net编程技术中的旋转函数Rotate Transform()法和计算坐标的方法来编写了船舶仪表控件中的电流表,介绍了两种不同编写方法的思考路径,阐述了这两种编写转动仪表控件方法的优点和缺点。

Numerical simulation of seismic wavefields in TTI media using the rotated staggered-grid compact finite-difference scheme

Numerical simulation in transverse isotropic media with tilted symmetry axis（TTI） using the standard staggered-grid finite-difference scheme（SSG）results in errors caused by averaging or interpolation. In order to eliminate the errors, a method of rotated staggered-grid finite-difference scheme（RSG） is proposed. However, the RSG brings serious numerical dispersion. The compact staggered-grid finite-difference scheme（CSG） is an implicit difference scheme, which use fewer grid points to suppress dispersion more effectively than the SSG. This paper combines the CSG with the RSG to derive a rotated staggered-grid compact finite-difference scheme（RSGC）. The numerical experiments indicate that the RSGC has weaker numerical dispersion and better accuracy than the RSG.

Improvement of visual acuity in children with anisometropic amblyopia treated with rotated prisms combined with near activity

·AIM: To evaluate the efficacy of a new modality for improving visual acuity (VA) in pediatric patients with anisometropic amblyopia. · METHODS: Retrospective and interventional case series. Medical records of 360 children with anisometropic amblyopia treated with a modality that included rotated prisms, lenses, and near activities from January 2008 to January 2012 were analyzed. Characteristics such as improvement of VA and contrast sensitivity in amblyopic eyes and resolution of amblyopia (VA ≤ 0.1logMAR or a difference of ≤ 2 lines in logMAR between the eyes) were assessed. ·RESULTS: Among the patients, the mean VA of the amblyopic eyes improved from 0.48logMAR (SD=0.16) to 0.12logMAR (SD =0.16) and the mean VA improvement was 0.36logMAR (SD =0.10, P【0.001). Resolution of amblyopia was achieved in 233 of 360 patients (64.72%). The mean time for resolution of amblyopia was 8.05 weeks (SD=4.83) or 14.14 sessions (SD=8.76). Among the study group, refraction error did not change significantly after treatment (P=0.437). We found that better baseline VA may be related to success and shorten the time to amblyopic resolution. ·CONCLUSION: VA and contrast sensitivity improved with rotated prisms, correcting lenses, and near activities in children with anisometropic amblyopia. The VA improvement by this modality was comparable to other methods. However, the time to resolution of amblyopia was shorter with this method than with other modalities. Rotated prisms combined with near acuity could provide an alternative treatment in children with anisometropic amblyopia who can’t tolerant traditional therapy method like patching.

Diffraction Pattern of a Rotated Grating

Diffraction patterns of a rotated grating are investigated from both theoretical and experimental points of view. It is shown that as the grating rotates, the angle of deviation of each diffracted line relative to the incident light goes through a minimum, and that the angle between any two successive diffracted lines goes through a minimum value which is the same for all adjacent diffracted lines. It is also shown that the angle between diffraction lines with n=1 and n=-1 is not sensitive to small variations of the grating from being normal to the incident light. Finally, a method is suggested for determining the line distance of a diffraction grating with high accuracy.

Geochemistry and Geochronology of Circumferential Dykes of the Franklin LIP: A Rotated Perspective on Plate Reconstruction

In addition to an extrusive volcanic component and associated sills,the Neoproterozoic Franklin Large Igneous Province(LIP)comprises a giant radiating dyke swarm spanning an arc of ca.110?,as well as a less-

Compact Interlaced Dual Circularly Polarized Sequentially Rotated Dielectric-Resonator Antenna Array

In this study,a compact 2×2 interlaced sequentially rotated dual-polarized dielectric-resonator antenna array is proposed for 5.8 GHz applications.The array is composed of a novel unit elements that are made of rectangular dielectric resonator(RDR)coupled to an eye slot for generating the orthogonal modes,TEδx 21 and TE1yδ1 to acquire circular polarization(CP)radiation.For the purpose of miniaturization and achieving dual polarized resonance,the array is fed by two interlaced ports and each port excites two radiating elements.The first port feeds horizontal elements to obtain left hand circular polarization(LHCP).The second port feeds vertical elements to obtain right hand circular polarization(RHCP).A quarter-wave length transformer is employed to reduce the attenuation and consequently increase the array gain performance.The 35×35 mm2(0.676λ0×0.676λ0)gains were 8.4 and 8.2 dBi for port 1 and port 2,respectively,with port isolations of−33.51 dB.The design achieves a voltage standing-wave ratio(VSWR)<−10 dB and an axial ratio(AR)<−3 dB bandwidth of 2.48%(5.766 to 5.911 GHz)for LHCP at port 1 and a VSWR<−10 dB and AR<−3 dB bandwidth of 2.28%(5.788 to 5.922 GHz)for RHCP at port 2.The findings of the proposed design validate its use for ISM band applications.

Learning power Gaussian modeling loss for dense rotated object detection in remote sensing images

Object detection in Remote Sensing(RS)has achieved tremendous advances in recent years,but it remains challenging for rotated object detection due to cluttered backgrounds,dense object arrangements and the wide range of size variations among objects.To tackle this problem,Dense Context Feature Pyramid Network(DCFPN)and a powerα-Gaussian loss are designed for rotated object detection in this paper.The proposed DCFPN can extract multi-scale information densely and accurately by leveraging a dense multi-path dilation layer to cover all sizes of objects in remote sensing scenarios.For more accurate detection while avoiding bottlenecks such as boundary discontinuity in rotated bounding box regression,a-Gaussian loss,a unified power generalization of existing Gaussian modeling losses is proposed.Furthermore,the properties ofα-Gaussian loss are analyzed comprehensively for a wider range of applications.Experimental results on four datasets(UCAS-AOD,HRSC2016,DIOR-R,and DOTA)show the effectiveness of the proposed method using different detectors,and are superior to the existing methods in both feature extraction and bounding box regression。

RB-SLAM:visual SLAM based on rotated BEBLID feature point description

The extraction and description of image features are very important for visual simultaneous localization and mapping(V-SLAM).A rotated boosted efficient binary local image descriptor(BEBLID)SLAM(RB-SLAM)algorithm based on improved oriented fast and rotated brief(ORB)feature description is proposed in this paper,which can solve the problems of low localization accuracy and time efficiency of the current ORB-SLAM3 algorithm.Firstly,it uses the BEBLID to replace the feature point description algorithm of the original ORB to enhance the expressiveness and description efficiency of the image.Secondly,it adds rotational invariance to the BEBLID using the orientation information of the feature points.It also selects the rotationally stable bits in the BEBLID to further enhance the rotational invariance of the BEBLID.Finally,it retrains the binary visual dictionary based on the BEBLID to reduce the cumulative error of V-SLAM and improve the loading speed of the visual dictionary.Experiments show that the dictionary loading efficiency is improved by more than 10 times.The RB-SLAM algorithm improves the trajectory accuracy by 24.75%on the TUM dataset and 26.25%on the EuRoC dataset compared to the ORB-SLAM3 algorithm.

CONSTRAINED QUADRILATERAL NONCONFORMING ROTATED Q1 ELEMENT

In this paper, we define a new nonconforming quadrilateral finite element based on the nonconforming rotated Q1 element by enforcing a constraint on each element, which has only three degrees of freedom. We investigate the consistency, approximation, superclose property, discrete Green＇s function and superconvergence of this element. Moreover, we propose a new postprocessing technique and apply it to this element. It is proved that the postprocessed discrete solution is superconvergent under a mild assumption on the mesh.

NONCONFORMING QUADRILATERAL ROTATED ELEMENT FOR REISSNER-MINDLIN PLATE

In this paper, we extend two rectangular elements for Reissner-Mindlin plate [9] to the quadrilateral case. Optimal H and L error bounds independent of the plate hickness are derived under a mild assumption on the mesh partition.

A V-CYCLE MUTIGRID FOR QUADRILATERAL ROTATED Q_1 ELEMENT WITH NUMERICAL INTEGRATION

In this paper, a V-cycle multigrid method is presented for quadrilateral rotated elements with numerical integration.

MATHEMATICAL ANALYSIS FOR QUADRILATERAL ROTATED Q_1 ELEMENT Ⅲ: THE EFFECT OF NUMERICAL INTEGRATION

This is the third part of the paper for the rotated Q1 nonconforming element on quadrilateral meshes for general second order elliptic problems. Some optimal numerical formulas are presented and analyzed. The novelty is that it includes a formula with only two sampling points which excludes even a Q1 unisolvent set. It is the optimal numerical integration formula over a quadrilateral mesh with least sampling points up to now.

ROTATED COMPLEX EMPIRICAL ORTHOGONAL FUNCTION(RCEOF)ANALYSIS:THEORY AND EXAMPLES—PART I

In this paper,a new diagnostic method,the rotated complex empirical orthogonal function (RCEOF)analysis is developed.The general principle and the mathematical foundation of RCEOF are discussed.

MATHEMATICAL ANALYSIS FOR QUADRILATERAL ROTATED Q_1 ELEMENT Ⅱ: POINCARE INEQUALITY AND TRACE INEQUALITY

This is the second part of the paper for the mathematical study of nonconforming rotated Q1 element (NRQ1 hereafter) on arbitrary quadrilateral meshes. Some Poincare Inequalities are proved without assuming the quasi-uniformity of the mesh subdivision. A discrete trace inequality is also proved.

Nonconforming rotated Q_1 element on non-tensor product anisotropic meshes

In this paper, we consider the nonconforming rotated Q1 element for the second order elliptic problem on the non-tensor product anisotropic meshes, i.e. the anisotropic affine quadrilateral meshes. Though the interpolation error is divergent on the anisotropic meshes,we overcome this difficulty by constructing another proper operator. Then we give the optimal approximation error and the consistency error estimates under the anisotropic affine quadrilateral meshes. The results of this paper provide some hints to derive the anisotropic error of some finite elements whose interpolations do not satisfy the anisotropic interpolation properties. Lastly, a numerical test is carried out, which coincides with our theoretical analysis.

Multi-blade rubbing characteristics of the shaft-disk-blade-casing system with large rotation

Blade rubbing faults cause detrimental impact on the operation of aeroengines. Most of the existing studies on blade rubbing in the shaft-disk-blade-casing(SDBC) system have overlooked the elastic deformation of the blade, while some only consider the whirl of the rotor, neglecting its spin. To address these limitations, this paper proposes a dynamic model with large rotation for the SDBC system. The model incorporates the spin and whirl of the rotor, enabling the realistic reproduction of multiblade rubbing faults. To verify the accuracy of the SDBC model with large rotation and demonstrate its capability to effectively consider the rotational effects such as the centrifugal stiffening and gyroscopic effects, the natural characteristics and dynamic responses of the proposed model are compared with those obtained from reported research and experimental results. Furthermore, the effects of the rotating speed, contact stiffness,and blade number on the dynamic characteristics of the SDBC system with multi-blade rubbing are investigated. The results indicate that the phase angle between the rotor deflection and the unbalance excitation force increases with the increasing rotating speed,which significantly influences the rubbing penetration of each blade. The natural frequency of the SDBC system with rubbing constrain can be observed in the acceleration response of the casing and the torsional response of the shaft, and the frequency is related to the contact stiffness. Moreover, the vibration amplitude increases significantly with the product of the blade number under rubbing, and the rotating frequency approaches the natural frequency of the SDBC system. The proposed model can provide valuable insight for the fault diagnosis of rubbing in bladed rotating machinery.

ROTATED COMPLEX EMPIRICAL ORTHOGONAL FUNCTION(RCEOF)ANALYSIS—PART Ⅱ:THEORY AND EXAMPLES

The numerical solving and the program designing of the rotated complex empirical orthogonal function(RCEOF)are discussed.Some examples of RCEOF are also presented.

Modulation of High-Order Harmonic Generation from a Monolayer ZnO by Co-rotating Two-Color Circularly Polarized Laser Fields

By numerically solving the two-dimensional semiconductor Bloch equation,we study the high-order harmonic emission of a monolayer ZnO under the driving of co-rotating two-color circularly polarized laser pulses.By changing the relative phase between the fundamental frequency field and the second one,it is found that the harmonic intensity in the platform region can be significantly modulated.In the higher order,the harmonic intensity can be increased by about one order of magnitude.Through time-frequency analysis,it is demonstrated that the emission trajectory of monolayer ZnO can be controlled by the relative phase,and the harmonic enhancement is caused by the second quantum trajectory with the higher emission probability.In addition,near-circularly polarized harmonics can be generated in the co-rotating two-color circularly polarized fields.With the change of the relative phase,the harmonics in the platform region can be altered from left-handed near-circularly polarization to right-handed one.Our results can obtain high-intensity harmonic radiation with an adjustable ellipticity,which provides an opportunity for syntheses of circularly polarized attosecond pulses.