We present a general variational approach to determine the steady state of open quantum lattice systems via a neural-network approach. The steady-state density matrix of the lattice system is ...constructed via a purified neural-network Ansatz in an extended Hilbert space with ancillary degrees of freedom. The variational minimization of cost functions associated to the master equation can be performed using a Markov chain Monte Carlo sampling. As a first application and proof of principle, we apply the method to the dissipative quantum transverse Ising model.
Unmanned aerial vehicle (UAV) object tracking has been widely used in military and civilian tasks and is very challenging due to factors such as aerial view, low resolution (LR), background clutter ...(BC), and small scale. Currently, many correlation filter (CF) methods for UAV object tracking introduce predefined regularization terms to improve the discriminative power. However, the predefined spatial constraints neither exploit the changing foreground and background information during tracking nor adapt to complex video attributes, such as BC, illumination variation (IV), and viewpoint change (VC). In this work, a novel CF tracking model is proposed to learn the spatial regularization CFs with the Hilbert-Schmidt independence criterion (HSIC_SRCF) in the reproducing kernel Hilbert space (RKHS) for UAV tracking. First, HSIC _SRCF learns the high confidence spatial weight coefficient for the filters, which encourages the filters to focus on the more reliable region. Second, the alternative direction method of multipliers (ADMM) can be used to optimize the proposed model, and the subproblems of the model have closed-form solutions. Third, the model update scheme uses RKHS and the peak-to-sidelobe ratio (PSR) to obtain the confidence of the object bounding box and reduce the effect of background noise for the UAV object. The ablation study shows that the proposed approach achieves a precision of 0.699 and a success rate of 0.607, which are 2.8% higher and 2.2% higher, respectively, than the baseline AutoTrack on the UAV123@10fps. Experimental results on four popular UAV datasets, including VisDrone2018-test-dev, UAV123@10fps, UAV123, and UAVDT, show that our approach performs favorably compared with current state-of-the-art methods.
A basic idea of quantum computing is surprisingly similar to that of kernel methods in machine learning, namely, to efficiently perform computations in an intractably large Hilbert space. In this ...Letter we explore some theoretical foundations of this link and show how it opens up a new avenue for the design of quantum machine learning algorithms. We interpret the process of encoding inputs in a quantum state as a nonlinear feature map that maps data to quantum Hilbert space. A quantum computer can now analyze the input data in this feature space. Based on this link, we discuss two approaches for building a quantum model for classification. In the first approach, the quantum device estimates inner products of quantum states to compute a classically intractable kernel. The kernel can be fed into any classical kernel method such as a support vector machine. In the second approach, we use a variational quantum circuit as a linear model that classifies data explicitly in Hilbert space. We illustrate these ideas with a feature map based on squeezing in a continuous-variable system, and visualize the working principle with two-dimensional minibenchmark datasets.
Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, ...densities do not live in a vector space and, therefore, commonly used Hubert space based methods of functional data analysis are not applicable. To address this problem, we introduce a transformation approach, mapping probability densities to a Hubert space of functions through a continuous and invertible map. Basic methods of functional data analysis, such as the construction of functional modes of variation, functional regression or classification, are then implemented by using representations of the densities in this linear space. Representations of the densities themselves are obtained by applying the inverse map from the linear functional space to the density space. Transformations of interest include log quantile density and log hazard transformations, among others. Rates of convergence are derived for the representations that are obtained for a general class of transformations under certain structural properties. If the subjectspecific densities need to be estimated from data, these rates correspond to the optimal rates of convergence for density estimation. The proposed methods are illustrated through simulations and applications in brain imaging.
Functional Bayesian Filter Li, Kan; Principe, Jose C.
IEEE transactions on signal processing,
2022, Volume:
70
Journal Article
Peer reviewed
Open access
We present a general nonlinear Bayesian filter for high-dimensional state estimation using the theory of reproducing kernel Hilbert space (RKHS). By applying the kernel method and the representer ...theorem to perform linear quadratic estimation in a functional space, we derive a Bayesian recursive state estimator for a general nonlinear dynamical system in the original input space. Unlike existing nonlinear extensions of the Kalman filter where the system dynamics are assumed known, the state-space representation for the Functional Bayesian Filter (FBF) is completely learned online from measurement data in the form of an infinite impulse response (IIR) filter or recurrent network in the RKHS, with universal approximation property. Using a positive definite kernel function satisfying Mercer's conditions to compute and evolve information quantities, the FBF exploits both the statistical and time-domain information about the signal, extracts higher-order moments, and preserves the properties of covariances without the ill effects due to conventional arithmetic operations. We apply this novel kernel adaptive filtering (KAF) to recurrent network training, chaotic time-series estimation and cooperative filtering using Gaussian and non-Gaussian noises, and inverse kinematics modeling. Simulation results show FBF outperforms existing Kalman-based algorithms.
Optimal measurements for the discrimination of quantum states are useful tools for classification problems. In order to exploit the potential of quantum computers, feature vectors have to be encoded ...into quantum states represented by density operators. However, quantum-inspired classifiers based on nearest mean and on Helstrom state discrimination are implemented on classical computers. We show a geometric approach that improves the efficiency of quantum-inspired classification in terms of space and time acting on quantum encoding and allows one to compare classifiers correctly in the presence of multiple preparations of the same quantum state as input. We also introduce the nearest mean classification based on Bures distance, Hellinger distance and Jensen-Shannon distance comparing the performance with respect to well-known classifiers applied to benchmark datasets.
A central challenge in quantum computing is to identify more computational problems for which utilization of quantum resources can offer significant speedup. Here, we propose a hybrid ...quantum-classical scheme to tackle the quantum optimal control problem. We show that the most computationally demanding part of gradient-based algorithms, namely, computing the fitness function and its gradient for a control input, can be accomplished by the process of evolution and measurement on a quantum simulator. By posing queries to and receiving answers from the quantum simulator, classical computing devices update the control parameters until an optimal control solution is found. To demonstrate the quantum-classical scheme in experiment, we use a seven-qubit nuclear magnetic resonance system, on which we have succeeded in optimizing state preparation without involving classical computation of the large Hilbert space evolution.
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