Related papers: Kernel controlled real-time Complex Langevin simul…

We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…

The support vector machine (SVM) is a popular machine learning classification method which produces a nonlinear decision boundary in a feature space by constructing linear boundaries in a transformed Hilbert space. It is well known that…

Efficient quantum compiling tactics greatly enhance the capability of quantum computers to execute complicated quantum algorithms. Due to its fundamental importance, a plethora of quantum compilers has been designed in past years. However,…

Machine learning is applied to investigate the phase transition of two-dimensional complex plasmas. The Langevin dynamics simulation is employed to prepare particle suspensions in various thermodynamic states. Based on the resulted particle…

Computing the viability kernel is key in providing guarantees of safety and proving existence of safety-preserving controllers for constrained dynamical systems. Current numerical techniques that approximate this construct suffer from a…

The kernel trick is a widely applicable technique in machine learning domains that maps datasets that are difficult to classify into a computationally friendly feature space. As the dimension of the dataset scales, these kernel calculations…

Linear-scaling electronic structure methods based on the calculation of moments of the underlying electronic Hamiltonian offer a computationally efficient and numerically robust scheme to drive large-scale atomistic simulations, in which…

Quantum kernel methods have been proposed as a promising approach for leveraging near-term quantum computers for supervised learning, yet rigorous benchmarks against strong classical baselines remain scarce. We present a comprehensive…

A quantum-mechanical system comes naturally equipped with a convex space: each (Hermitian) operator has a (real) expectation value, and the expectation value of the square any Hermitian operator must be non-negative. This space is of…

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…

We experimentally simulate the spin networks -- a fundamental description of quantum spacetime at the Planck level. We achieve this by simulating quantum tetrahedra and their interactions. The tensor product of these quantum tetrahedra…

Approximation of non-linear kernels using random feature maps has become a powerful technique for scaling kernel methods to large datasets. We propose $\textit{Tensor Sketch}$, an efficient random feature map for approximating polynomial…

We propose a novel kinetic Langevin sampler based on a specific splitting scheme using the exact harmonic Langevin integrator. For strongly log-concave target measures, the sampler exploits a decomposition of the strongly convex potential…

Quantum simulation - the use of one quantum system to simulate a less controllable one - may provide an understanding of the many quantum systems which cannot be modeled using classical computers. Impressive progress on control and…

We introduce a powerful iterative algorithm to compute protein folding pathways, with realistic all-atom force fields. Using the path integral formalism, we explicitly derive a modified Langevin equation which samples directly the ensemble…

We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The…

Langevin and Brownian simulations play a prominent role in computational research, and state of the art integration algorithms provide trajectories with different stability ranges and accuracy in reproducing statistical averages. The…

We present a geometric formulation of the Multiple Kernel Learning (MKL) problem. To do so, we reinterpret the problem of learning kernel weights as searching for a kernel that maximizes the minimum (kernel) distance between two convex…

Stationary distributions of complex Langevin equations are shown to be the complexified path integral solutions of the Schwinger-Dyson equations of the associated quantum field theory. Specific examples in zero dimensions and on a lattice…

While historically many quantum mechanical simulations of molecular dynamics have relied on the Born-Oppenheimer approximation to separate electronic and nuclear behavior, recently a lot of interest has arisen towards quantum effects in…