Gyarfas conjectured in 2011 that every $r$-edge-colored $K_n$ contains a monochromatic component of bounded (perhaps three) diameter on at least $n/(r-1)$ vertices. Letzter proved this conjecture with diameter four. In this note we improve the re
sult in the case of $r=3$: We show that in every $3$-edge-coloring of $K_n$ either there is a monochromatic component of diameter at most three on at least $n/2$ vertices or every color class is spanning and has diameter at most four.
Coupled cluster Greens function (CCGF) approach has drawn much attention in recent years for targeting the molecular and material electronic structure problems from a many-body perspective in a systematically improvable way. Here, we will present a b
rief review of the history of how the Greens function method evolved with the wavefunction, early and recent development of CCGF theory, and more recently scalable CCGF software development. We will highlight some of the recent applications of CCGF approach and propose some potential applications that would emerge in the near future.
This paper presents a summary of the DFGC 2021 competition. DeepFake technology is developing fast, and realistic face-swaps are increasingly deceiving and hard to detect. At the same time, DeepFake detection methods are also improving. There is a tw
o-party game between DeepFake creators and detectors. This competition provides a common platform for benchmarking the adversarial game between current state-of-the-art DeepFake creation and detection methods. In this paper, we present the organization, results and top solutions of this competition and also share our insights obtained during this event. We also release the DFGC-21 testing dataset collected from our participants to further benefit the research community.
Topological phases of matter have revolutionized the fundamental understanding of band theory and hold great promise for next-generation technologies such as low-power electronics or quantum computers. Single-gap topologies have been extensively expl
ored, and a large number of materials have been theoretically proposed and experimentally observed. These ideas have recently been extended to multi-gap topologies, characterized by invariants that arise by the momentum space braiding of band nodes that carry non-Abelian charges. However, the constraints placed by the Fermi-Dirac distribution to electronic systems have so far prevented the experimental observation of multi-gap topologies in real materials. Here, we show that multi-gap topologies and the accompanying phase transitions driven by braiding processes can be readily observed in the bosonic phonon spectra of known monolayer silicates. The associated braiding process can be controlled by means of an electric field and epitaxial strain, and involves, for the first time, more than three bands. Finally, we propose that these conversion processes can be tracked by following the evolution of the Raman spectrum, providing a clear signature for the experimental verification of multi-gap topologies.
In recent years, virtual makeup applications have become more and more popular. However, it is still challenging to propose a robust makeup transfer method in the real-world environment. Current makeup transfer methods mostly work well on good-condit
ioned clean makeup images, but transferring makeup that exhibits shadow and occlusion is not satisfying. To alleviate it, we propose a novel makeup transfer method, called 3D-Aware Shadow and Occlusion Robust GAN (SOGAN). Given the source and the reference faces, we first fit a 3D face model and then disentangle the faces into shape and texture. In the texture branch, we map the texture to the UV space and design a UV texture generator to transfer the makeup. Since human faces are symmetrical in the UV space, we can conveniently remove the undesired shadow and occlusion from the reference image by carefully designing a Flip Attention Module (FAM). After obtaining cleaner makeup features from the reference image, a Makeup Transfer Module (MTM) is introduced to perform accurate makeup transfer. The qualitative and quantitative experiments demonstrate that our SOGAN not only achieves superior results in shadow and occlusion situations but also performs well in large pose and expression variations.
The synthetic dimension, a research topic of both fundamental significance and practical applications, is attracting increasing attention in recent years. In this paper, we propose a theoretical framework to construct arbitrary synthetic dimensions,
or N-boson synthetic lattices, using multiple bosons on one-dimensional lattices. We show that a one-dimensional lattice hosting N indistinguishable bosons can be mapped to a single boson on a N-dimensional lattice with high symmetry. Band structure analyses on this N-dimensional lattice can then be mathematically performed to predict the existence of exotic eigenstates and the motion of N-boson wavepackets. As illustrative examples, we demonstrate the edge states in two-boson Su-Schrieffer-Heeger synthetic lattices without interactions, interface states in two-boson Su-Schrieffer-Heeger synthetic lattices with interactions, and weakly-bound triplon states in three-boson tight-binding synthetic lattices with interactions. The interface states and weakly-bound triplon states have not been thoroughly understood in previous literatures. Our proposed theoretical framework hence provides a novel perspective to explore the multi-boson dynamics on lattices with boson-boson interactions, and opens up a future avenue in the fields of multi-boson manipulation in quantum engineering.
Observations of Interplanetary Scintillation (IPS) are an efficient remote-sensing method to study the solar wind and inner heliosphere. From 2016 to 2018, some distinctive observations of IPS sources like 3C 286 and 3C 279 were accomplished with the
Five-hundred-meter Aperture Spherical radio Telescope (FAST), the largest single-dish telescope in the world. Due to the 270-1620 MHz wide frequency coverage of the Ultra-Wideband (UWB) receiver, one can use both single-frequency and dual-frequency analyses to determine the projected velocity of the solar wind. Moreover, based on the extraordinary sensitivity owing to the large collecting surface area of FAST, we can observe weak IPS signals. With the advantages of both the wider frequency coverage and high sensitivity, also with our radio frequency interference (RFI) mitigation strategy and an optimized model-fitting method developed, in this paper, we analyze the fitting confidence intervals of the solar wind velocity, and present some preliminary results achieved using FAST, which points to the current FAST system being highly capable of carrying out observations of IPS
The three key elements of a quantum simulation are state preparation, time evolution, and measurement. While the complexity scaling of dynamics and measurements are well known, many state preparation methods are strongly system-dependent and require
prior knowledge of the systems eigenvalue spectrum. Here, we report on a quantum-classical implementation of the coupled-cluster Greens function (CCGF) method, which replaces explicit ground state preparation with the task of applying unitary operators to a simple product state. While our approach is broadly applicable to a wide range of models, we demonstrate it here for the Anderson impurity model (AIM). The method requires a number of T gates that grows as $ mathcal{O} left(N^5 right)$ per time step to calculate the impurity Greens function in the time domain, where $N$ is the total number of energy levels in the AIM. For comparison, a classical CCGF calculation of the same order would require computational resources that grow as $ mathcal{O} left(N^6 right)$ per time step.
The variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues and eigenvalues of a Hamiltonian. VQE has been proposed as an alternative to fully quantum algorithms such as quantu
m phase estimation because fully quantum algorithms require quantum hardware that will not be accessible in the near future. VQE has been successfully applied to solve the electronic Schr{o}dinger equation for a variety of small molecules. However, the scalability of this method is limited by two factors: the complexity of the quantum circuits and the complexity of the classical optimization problem. Both of these factors are affected by choice of the variational ansatz used to represent the trial wave function. Hence, the construction of efficacious ansatz is an active area of research. Put another way, modern quantum computers are not capable of executing deep quantum circuits produced by using currently available ansatze for problems that map onto more than several qubits. In this review, we present recent developments in the field of designing effective ansatzes that fall into two categories -- chemistry inspired and hardware efficient -- that produce quantum circuits that are easier to run on modern hardware. We discuss the shortfalls of ansatzes originally formulated for VQE simulations, how they are addressed in more sophisticated methods, and the potential ways for further improvements.
The notion of topological phases extended to dynamical systems stimulates extensive studies, of which the characterization of non-equilibrium topological invariants is a central issue and usually necessitates the information of quantum dynamics in bo
th the time and spatial dimensions. Here we combine the recently developed concepts of the dynamical classification of topological phases and synthetic dimension, and propose to efficiently characterize photonic topological phases via holographic quench dynamics. A pseudo spin model is constructed with ring resonators in a synthetic lattice formed by frequencies of light, and the quench dynamics is induced by initializing a trivial state which evolves under a topological Hamiltonian. Our key prediction is that the complete topological information of the Hamiltonian is extracted from quench dynamics solely in the time domain, manifesting holographic features of the dynamics. In particular, two fundamental time scales emerge in the quench dynamics, with one mimicking the Bloch momenta of the topological band and the other characterizing the residue time evolution of the state after quench. For this a dynamical bulk-surface correspondence is obtained in time dimension and characterizes the topology of the spin model. This work also shows that the photonic synthetic frequency dimension provides an efficient and powerful way to explore the topological non-equilibrium dynamics.
