Related papers: Solving the Liouvillian Gap with Artificial Neural…

In the paper, we introduce several accelerate iterative algorithms for solving the multiple-set split common fixed-point problem of quasi-nonexpansive operators in real Hilbert space. Based on primal-dual method, we construct several…

It remains a challenge to simultaneously remove geometric distortion and space-time-varying blur in frames captured through a turbulent atmospheric medium. To solve, or at least reduce these effects, we propose a new scheme to recover a…

Adiabatic state preparation provides an analytical solution for generating the ground state of a target Hamiltonian, starting from an easily prepared ground state of the initial Hamiltonian. While effective for time-dependent Hamiltonians…

The motivation for studying non-Hermitian systems and the role of $\mathcal{PT}$-symmetry is discussed. We investigate the use of a quantum algorithm to find the eigenvalues and eigenvectors of non-Hermitian Hamiltonians, with applications…

Bayesian inference for high-dimensional inverse problems is computationally costly and requires selecting a suitable prior distribution. Amortized variational inference addresses these challenges via a neural network that approximates the…

Simulating the dynamics and the non-equilibrium steady state of an open quantum system are hard computational tasks on conventional computers. For the simulation of the time evolution, several efficient quantum algorithms have recently been…

We introduce a novel Bayesian phase estimation technique based on adaptive grid refinement method. This method automatically chooses the number particles needed for accurate phase estimation using grid refinement and cell merging strategies…

Originating from image recognition, methods of machine learning allow for effective feature extraction and dimensionality reduction in multidimensional datasets, thereby providing an extraordinary tool to deal with classical and quantum…

We introduce an iterative method to search for time-optimal Hamiltonians that drive a quantum system between two arbitrary, and in general mixed, quantum states. The method is based on the idea of progressively improving the efficiency of…

Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…

Graphical models are powerful tools for modeling high-dimensional data, but learning graphical models in the presence of latent variables is well-known to be difficult. In this work we give new results for learning Restricted Boltzmann…

We introduce a novel, model-independent method for the efficient simulation of low-entropy systems, whose dynamics can be accurately described with a limited number of states. Our method leverages the time-dependent variational principle to…

The adiabatic quantum algorithm has drawn intense interest as a potential approach to accelerating optimization tasks using quantum computation. The algorithm is most naturally realised in systems which support Hamiltonian evolution, rather…

Recent advances in deep learning and neural networks have led to an increased interest in the application of generative models in statistical and condensed matter physics. In particular, restricted Boltzmann machines (RBMs) and variational…

Consider a path of non-degenerate eigenstates of unitary operators or Hamiltonians with minimum eigenvalue gap G. The eigenpath traversal problem is to transform one or more copies of the initial to the final eigenstate. Solutions to this…

Restricted Boltzmann Machines (RBMs) and models derived from them have been successfully used as basic building blocks in deep artificial neural networks for automatic features extraction, unsupervised weights initialization, but also as…

In this paper we propose an adaptive scheme for the solution of time-dependent boundary value problems (BVPs). To solve numerically these problems, we consider the kernel-based method of lines that allows us to split the spatial and time…

Despite the success of diffusion models (DMs), we still lack a thorough understanding of their latent space. While image editing with GANs builds upon latent space, DMs rely on editing the conditions such as text prompts. We present an…

A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…

The development of quantum-classical hybrid (QCH) algorithms is critical to achieve state-of-the-art computational models. A QCH variational autoencoder (QVAE) was introduced in Ref. [1] by some of the authors of this paper. QVAE consists…