Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions

We study the anisotropic effect of the Coulomb interaction on a 1/3-filling fractional quantum Hall system by using an exact diagonalization method on small systems in torus geometry. For weak anisotropy the system remains to be an incompressible quantum liquid, although anisotropy manifests itself in density correlation functions and excitation spectra. When the strength of anisotropy increases, we find the system develops a Hall-smectic-like phase with a one-dimensional charge density wave order and is unstable towards the one-dimensional crystal in the strong anisotropy limit. In all three phases of the Laughlin liquid, Hall-smectic-like, and crystal phases the ground state of the anisotropic Coulomb system can be well described by a family of model wave functions generated by an anisotropic projection Hamiltonian. We discuss the relevance of the results to the geometrical description of fractional quantum Hall states proposed by Haldane [ Phys. Rev. Lett. 107 116801 (2011)].Comment: 8 pages, 8 figure

Absence of barren plateaus in finite local-depth circuits with long-range entanglement

Ground state preparation is classically intractable for general Hamiltonians. On quantum devices, shallow parameterized circuits can be effectively trained to obtain short-range entangled states under the paradigm of variational quantum eigensolver, while deep circuits are generally untrainable due to the barren plateau phenomenon. In this Letter, we give a general lower bound on the variance of circuit gradients for arbitrary quantum circuits composed of local 2-designs. Based on our unified framework, we prove the absence of barren plateaus in training finite local-depth circuits for the ground states of local Hamiltonians. These circuits are allowed to be deep in the conventional definition of circuit depth so that they can generate long-range entanglement, but their local depths are finite, i.e., there is only a finite number of non-commuting gates acting on individual qubits. This fact suggests that long-range entangled ground states, such as topologically ordered states, are in general possible to be prepared efficiently on quantum devices via variational methods. We validate our analytical results with extensive numerical simulations and demonstrate the effectiveness of variational training using the generalized toric code model.Comment: 28 pages, 7 figure

The Relationship Between Investor Sentiment and Stock Market Volatility: Based on the VAR Model

Using web crawling technology crawls investors’ comments of SANY stock(Stock Code: 600031) and Fujian Expressway stock(Stock Code: 600033) from February 11, 2015 to August 16, 2017. Then using semi-supervised machine learning method construct investor sentiment index. Moreover, collecting the daily closing stock price and trading volume data from Qianlong software explore the relationship between investor sentiment and stock market volatility based on VAR model and Granger Test Method. The results show that the rate of return and trading volume have a two-way Granger causality, while negative emotion and the rate of return have a one-way Granger causality. Furthermore, with the impulse response function and variance decomposition, the results show that trading volume has significant effects on rate of return and negative emotions of investors have significant negative effects on rate of return and trading volume

Superradiant Transition to a Fermionic Quasicrystal in a Cavity

Recently, the steady state superradiance in degenerate Fermi gases has been realized in a cavity, following the previous discovery of the Dicke transition in Bose gases. The most prominent signature of fermionic Dicke transition is its density dependence, which is manifested as the Fermi surface nesting effect and the Pauli blocking effect. We study the superradiant transition in one-dimensional Fermi gases in a cavity with the presence of an incommensurate dipolar lattice. We find a first-order Dicke transition induced by indirect resonance effect, which is a resonance between two atomic levels by the level repulsion from a third level, and causes extra gap opening. By formulating a phenomenological theory, we find that the critical pumping strength for this first-order Dicke transition shows a linear V-shape kink near a particular indirect resonance modified filling $\nu_{\rm IRM}$. The presence and the unique density dependence of this transition manifest the fermionic nature and verify the mechanism of the quasicrystal superradiant transition.Comment: 5+8 pages, 3+6 figure

BiRA-Net: Bilinear Attention Net for Diabetic Retinopathy Grading

Diabetic retinopathy (DR) is a common retinal disease that leads to blindness. For diagnosis purposes, DR image grading aims to provide automatic DR grade classification, which is not addressed in conventional research methods of binary DR image classification. Small objects in the eye images, like lesions and microaneurysms, are essential to DR grading in medical imaging, but they could easily be influenced by other objects. To address these challenges, we propose a new deep learning architecture, called BiRA-Net, which combines the attention model for feature extraction and bilinear model for fine-grained classification. Furthermore, in considering the distance between different grades of different DR categories, we propose a new loss function, called grading loss, which leads to improved training convergence of the proposed approach. Experimental results are provided to demonstrate the superior performance of the proposed approach.Comment: Accepted at ICIP 201