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It is often the case that, while the numerical solution of the non-linear dispersive equation $\mathrm{i}\partial_t u(t)=\mathcal{H}(u(t),t)u(t)$ represents a formidable challenge, it is fairly easy and cheap to solve closely related linear equations of the form $\mathrm{i}\partial_t u(t)=\mathcal{H}_1(t)u(t)+\widetilde{\mathcal H}_2(t)u(t)$, where $\mathcal{H}_1(t)+\mathcal{H}_2(v,t)=\mathcal{H}(v,t)$. In that case we advocate an iterative linearisation procedure that involves fixed-point iteration of the latter equation to solve the former. A typical case is when the original problem is a nonlinear Schr\"odinger or Gross--Pitaevskii equation, while the `easy' equation is linear Schr\"odinger with time-dependent potential. We analyse in detail the iterative scheme and its practical implementation, prove that each iteration increases the order, derive upper bounds on the speed of convergence and discuss in the case of nonlinear Schr\"odinger equation with cubic potential the preservation of structural features of the underlying equation: the $\mathrm{L}_2$ norm, momentum and Hamiltonian energy. A key ingredient in our approach is the use of the Magnus expansion in conjunction with Hermite quadratures, which allows effective solutions of the linearised but non-autonomous equations in an iterative fashion. The resulting Magnus--Hermite methods can be combined with a wide range of numerical approximations to the matrix exponential. The paper concludes with a number of numerical experiments, demonstrating the power of the proposed approach., Comment: 23 pages, 5 figures

We develop a fourth-order Magnus expansion based quantum algorithm for the simulation of many-body problems involving two-level quantum systems with time-dependent Hamiltonians, $\mathcal{H}(t)$. A major hurdle in the utilization of the Magnus expansion is the appearance of a commutator term which leads to prohibitively long circuits. We present a technique for eliminating this commutator and find that a single time-step of the resulting algorithm is only marginally costlier than that required for time-stepping with a time-independent Hamiltonian, requiring only three additional single-qubit layers. For a large class of Hamiltonians appearing in liquid-state nuclear magnetic resonance (NMR) applications, we further exploit symmetries of the Hamiltonian and achieve a surprising reduction in the expansion, whereby a single time-step of our fourth-order method has a circuit structure and cost that is identical to that required for a fourth-order Trotterized time-stepping procedure for time-independent Hamiltonians. Moreover, our algorithms are able to take time-steps that are larger than the wavelength of oscillation of the time-dependent Hamiltonian, making them particularly suited for highly-oscillatory controls. The resulting quantum circuits have shorter depths for all levels of accuracy when compared to first and second-order Trotterized methods, as well as other fourth-order Trotterized methods, making the proposed algorithm a suitable candidate for simulation of time-dependent Hamiltonians on near-term quantum devices., Comment: 53 pages, 17 figures

In recent years deep learning methods have shown great superiority in compressed video quality enhancement tasks. Existing methods generally take the raw video as the ground truth and extract practical information from consecutive frames containing various artifacts. However, they do not fully exploit the valid information of compressed and raw videos to guide the quality enhancement for compressed videos. In this paper, we propose a unique Valid Information Guidance scheme (VIG) to enhance the quality of compressed videos by mining valid information from both compressed videos and raw videos. Specifically, we propose an efficient framework, Compressed Redundancy Filtering (CRF) network, to balance speed and enhancement. After removing the redundancy by filtering the information, CRF can use the valid information of the compressed video to reconstruct the texture. Furthermore, we propose a progressive Truth Guidance Distillation (TGD) strategy, which does not need to design additional teacher models and distillation loss functions. By only using the ground truth as input to guide the model to aggregate the correct spatio-temporal correspondence across the raw frames, TGD can significantly improve the enhancement effect without increasing the extra training cost. Extensive experiments show that our method achieves the state-of-the-art performance of compressed video quality enhancement in terms of accuracy and efficiency.

Video super-resolution is one of the most popular tasks on mobile devices, being widely used for an automatic improvement of low-bitrate and low-resolution video streams. While numerous solutions have been proposed for this problem, they are usually quite computationally demanding, demonstrating low FPS rates and power efficiency on mobile devices. In this Mobile AI challenge, we address this problem and propose the participants to design an end-to-end real-time video super-resolution solution for mobile NPUs optimized for low energy consumption. The participants were provided with the REDS training dataset containing video sequences for a 4X video upscaling task. The runtime and power efficiency of all models was evaluated on the powerful MediaTek Dimensity 9000 platform with a dedicated AI processing unit capable of accelerating floating-point and quantized neural networks. All proposed solutions are fully compatible with the above NPU, demonstrating an up to 500 FPS rate and 0.2 [Watt / 30 FPS] power consumption. A detailed description of all models developed in the challenge is provided in this paper., Comment: arXiv admin note: text overlap with arXiv:2105.08826, arXiv:2105.07809, arXiv:2211.04470, arXiv:2211.03885

The Fe-based superconductor Fe (Se,Te) combines non-trivial topology with unconventional superconductivity and may be an ideal platform to realize exotic states such as high-order topological corner modes and Majorana modes. Thin films of Fe (Se,Te) are important for device fabrication, phase sensitive transport measurements and for realizing proposals to engineer higher-order modes. However, while bulk Fe (Se,Te) has been extensively studied with a variety of techniques, the nature of the superconducting order parameter in the monolayer limit has not yet been explored. In this work, we study monolayer films of Fe (Se,Te) on Bi2Te3 with scanning tunneling spectroscopy and Bogoliubov quasiparticle interference (BQPI). We discover that the monolayer Fe (Se,Te)/Bi2Te3 heterostructures host a robust, multigap superconducting state that strongly resembles the bulk. BQPI maps at the gap energies show a strong spatial modulation, oriented 45 degrees to the Fe-Se bond direction. Analysis of the phase-referenced quasiparticle interference signal reveals a sign-changing s-wave order parameter similar to the bulk. Moreover, we observe a unique pattern of sign changes in the BQPI signal which have not been observed in the bulk. Our work establishes monolayer Fe (Se,Te)/Bi2Te3 as a robust multi-band unconventional superconductor and sets the stage for explorations of non-trivial topology in this highly-tunable system., Comment: 23 pages, 4 figures

This paper reviews the challenge on constrained high dynamic range (HDR) imaging that was part of the New Trends in Image Restoration and Enhancement (NTIRE) workshop, held in conjunction with CVPR 2022. This manuscript focuses on the competition set-up, datasets, the proposed methods and their results. The challenge aims at estimating an HDR image from multiple respective low dynamic range (LDR) observations, which might suffer from under- or over-exposed regions and different sources of noise. The challenge is composed of two tracks with an emphasis on fidelity and complexity constraints: In Track 1, participants are asked to optimize objective fidelity scores while imposing a low-complexity constraint (i.e. solutions can not exceed a given number of operations). In Track 2, participants are asked to minimize the complexity of their solutions while imposing a constraint on fidelity scores (i.e. solutions are required to obtain a higher fidelity score than the prescribed baseline). Both tracks use the same data and metrics: Fidelity is measured by means of PSNR with respect to a ground-truth HDR image (computed both directly and with a canonical tonemapping operation), while complexity metrics include the number of Multiply-Accumulate (MAC) operations and runtime (in seconds)., Comment: CVPR Workshops 2022. 15 pages, 21 figures, 2 tables

Monolayer 1T'-WTe2 is a quantum spin Hall insulator with a gapped bulk and gapless helical edge states persisting to temperatures around 100 K. Recent studies have revealed a topological-to-trivial phase transition as well the emergence of an unconventional, potentially topological superconducting state upon tuning the carrier concentration with gating. However, despite extensive studies, the effects of gating on the band structure and the helical edge states have not yet been established. In this work we present a combined low-temperature STM and first principles study of back-gated monolayer 1T'-WTe2 films grown on graphene. Consistent with a quantum spin Hall system, the films show well-defined bulk gaps and clear edge states that span the gap. By directly measuring the density of states with STM spectroscopy, we show that the bulk band gap magnitude shows substantial changes with applied gate voltage, which is contrary to the na\"ive expectation that a gate would rigidly shift the bands relative to the Fermi level. To explain our data, we carry out density functional theory and model Hamiltonian calculations which show that a gate electric field causes doping and inversion symmetry breaking which polarizes and spin-splits the bulk bands. Interestingly, the calculated spin splitting from the effective Rashba-like spin-orbit coupling can be in the tens of meV for the electric fields in the experiment, which may be useful for spintronics applications. Our work reveals the strong effect of electric fields on the bulk band structure of monolayer 1T'-WTe2, which will play a critical role in our understanding of gate-induced phenomena in this system., Comment: 15 pages, 5 figures

The electronic and magnetic properties of transition metal dichalcogenides are known to be extremely sensitive to their structure. In this paper we study the effect of structure on the electronic and magnetic properties of mono- and bilayer $VSe_2$ films grown using molecular beam epitaxy. $VSe_2$ has recently attracted much attention due to reports of emergent ferromagnetism in the 2D limit. To understand this important compound, high quality 1T and distorted 1T films were grown at temperatures of 200 $^\text{o}$C and 450 $^\text{o}$C respectively and studied using 4K Scanning Tunneling Microscopy/Spectroscopy. The measured density of states and the charge density wave (CDW) patterns were compared to band structure and phonon dispersion calculations. Films in the 1T phase reveal different CDW patterns in the first layer compared to the second. Interestingly, we find the second layer of the 1T-film shows a CDW pattern with 4a $\times$ 4a periodicity which is the 2D version of the bulk CDW observed in this compound. Our phonon dispersion calculations confirm the presence of a soft phonon at the correct wavevector that leads to this CDW. In contrast, the first layer of distorted 1T phase films shows a strong stripe feature with varying periodicities, while the second layer displays no observable CDW pattern. Finally, we find that the monolayer 1T $VSe_2$ film is weakly ferromagnetic, with ~ $3.5 {\mu}_B$ per unit similar to previous reports., Comment: 19 pages, 10 figures