Quantum Phase Recognition via Quantum Kernel Methods

The application of quantum computation to accelerate machine learning algorithms is one of the most promising areas of research in quantum algorithms. In this paper, we explore the power of quantum learning algorithms in solving an important class of Quantum Phase Recognition (QPR) problems, which are crucially important in understanding many-particle quantum systems. We prove that, under widely believed complexity theory assumptions, there exists a wide range of QPR problems that cannot be efficiently solved by classical learning algorithms with classical resources. Whereas using a quantum computer, we prove the efficiency and robustness of quantum kernel methods in solving QPR problems through Linear order parameter Observables. We numerically benchmark our algorithm for a variety of problems, including recognizing symmetry-protected topological phases and symmetry-broken phases. Our results highlight the capability of quantum machine learning in predicting such quantum phase transitions in many-particle systems

MixNN: A design for protecting deep learning models

In this paper, we propose a novel design, called MixNN, for protecting deep learning model structure and parameters. The layers in a deep learning model of MixNN are fully decentralized. It hides communication address, layer parameters and operations, and forward as well as backward message flows among non-adjacent layers using the ideas from mix networks. MixNN has following advantages: 1) an adversary cannot fully control all layers of a model including the structure and parameters, 2) even some layers may collude but they cannot tamper with other honest layers, 3) model privacy is preserved in the training phase. We provide detailed descriptions for deployment. In one classification experiment, we compared a neural network deployed in a virtual machine with the same one using the MixNN design on the AWS EC2. The result shows that our MixNN retains less than 0.001 difference in terms of classification accuracy, while the whole running time of MixNN is about 7.5 times slower than the one running on a single virtual machine

Tensor-network-assisted variational quantum algorithm

Near-term quantum devices generally suffer from shallow circuit depth and hence limited expressivity due to noise and decoherence. To address this, we propose tensor-network-assisted parametrized quantum circuits, which concatenate a classical tensor-network operator with a quantum circuit to effectively increase the circuit's expressivity without requiring a physically deeper circuit. We present a framework for tensor-network-assisted variational quantum algorithms that can solve quantum many-body problems using shallower quantum circuits. We demonstrate the efficiency of this approach by considering two examples of unitary matrix-product operators and unitary tree tensor networks, showing that they can both be implemented efficiently. Through numerical simulations, we show that the expressivity of these circuits is greatly enhanced with the assistance of tensor networks. We apply our method to two-dimensional Ising models and one-dimensional time-crystal Hamiltonian models with up to 16 qubits and demonstrate that our approach consistently outperforms conventional methods using shallow quantum circuits.Comment: 12 pages, 8 figures, 37 reference

On the Nature of Bifurcation in a Ratio-Dependent Predator-Prey Model with Delays

A ratio-dependent predator-prey model with two delays is investigated. The conditions which ensure the local stability and the existence of Hopf bifurcation at the positive equilibrium of the system are obtained. It shows that the two different time delays have different effects on the dynamical behavior of the system. An example together with its numerical simulations shows the feasibility of the main results. Finally, main conclusions are included

Complexity analysis of weakly noisy quantum states via quantum machine learning

Quantum computers capable of fault-tolerant operation are expected to provide provable advantages over classical computational models. However, the question of whether quantum advantages exist in the noisy intermediate-scale quantum era remains a fundamental and challenging problem. The root of this challenge lies in the difficulty of exploring and quantifying the power of noisy quantum states. In this work, we focus on the complexity of weakly noisy states, which we define as the size of the shortest quantum circuit required to prepare the noisy state. To analyze the complexity, we propose a quantum machine learning (QML) algorithm that exploits the intrinsic-connection property of structured quantum neural networks. The proposed QML algorithm enables efficiently predicting the complexity of weakly noisy states from measurement results, representing a paradigm shift in our ability to characterize the power of noisy quantum computation

The Effect of Time Delay on Dynamical Behavior in an Ecoepidemiological Model

A delayed predator-prey model with disease in the prey is investigated. The conditions for the local stability and the existence of Hopf bifurcation at the positive equilibrium of the system are derived. The effect of the two different time delays on the dynamical behavior has been given. Numerical simulations are performed to illustrate the theoretical analysis. Finally, the main conclusions are drawn