Related papers: Grassmann Time-Evolving Matrix Product Operators f…

When a quantum system couples strongly to multiple baths then it is generally no longer possible to describe the resulting system dynamics by simply adding the individual effects of each bath. However, capturing such multi-bath system…

We present a numerical method for studying the real time dynamics of a small interacting quantum system coupled to an infinite fermionic reservoir. By building an orthonormal basis in the operator space, we turn the Heisenberg equation of…

The signature transform is a 'universal nonlinearity' on the space of continuous vector-valued paths, and has received attention for use in machine learning on time series. However, real-world temporal data is typically observed at discrete…

I discuss a simple numerical algorithm for the direct evaluation of multiple Grassmann integrals. The approach is exact, suffers no Fermion sign problems, and allows arbitrarily complicated interactions. Memory requirements grow…

In this paper, we propose a novel machine learning method based on adaptive tensor neural network subspace to solve linear time-fractional diffusion-wave equations and nonlinear time-fractional partial integro-differential equations. In…

This article presents the first complete application of a quantum time-marching algorithm for simulating multidimensional linear transport phenomena with arbitrary boundaries, whereby the success probabilities are problem intrinsic. The…

A variation to the usual formulation of Grassmann representation path integrals is presented. Time-indexed anticommuting partners are introduced for each Grassmann coherent state variable and a general method for handling the effect of…

In this work we develop several new simulation algorithms for 1D many-body quantum mechanical systems combining the Matrix Product State variational ansatz with Taylor, Pade and Arnoldi approximations to the evolution operator. By comparing…

We introduce a systematic construction of higher-order matrix product operator (MPO) approximations of the time evolution operator for generic (short and long range) one-dimensional Hamiltonians. We demonstrate the utility of our…

The iterative algorithm recently proposed by Waxman for solving eigenvalue problems, which relies on the method of moments, has been modified to improve its convergence considerably without sacrificing its benefits or elegance. The…

Solving the Anderson impurity model typically involves a two-step process, where one first calculates the ground state of the Hamiltonian, and then computes its dynamical properties to obtain the Green's function. Here we propose a hybrid…

Ensuring safety is a key aspect in sequential decision making problems, such as robotics or process control. The complexity of the underlying systems often makes finding the optimal decision challenging, especially when the safety-critical…

Accurate thermodynamic simulations of correlated fermions using path integral Monte Carlo (PIMC) methods are of paramount importance for many applications such as the description of ultracold atoms, electrons in quantum dots, and warm-dense…

We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the…

Simulating time evolution of quantum systems is one of the most promising applications of quantum computing and also appears as a subroutine in many applications such as Green's function methods. In the current era of NISQ machines we…

In this paper, we consider the task of efficiently computing the numerical solution of evolutionary complex Ginzburg--Landau equations on Cartesian product domains with homogeneous Dirichlet/Neumann or periodic boundary conditions. To this…

Gaussian mixture models (GMMs) are fundamental tools in statistical and data sciences. We study the moments of multivariate Gaussians and GMMs. The $d$-th moment of an $n$-dimensional random variable is a symmetric $d$-way tensor of size…

$E(3)$-equivariant neural networks have proven to be effective in a wide range of 3D modeling tasks. A fundamental operation of such networks is the tensor product, which allows interaction between different feature types. Because this…

In general, matrix or tensor-valued functions are approximated using the method developed for vector-valued functions by transforming the matrix-valued function into vector form. This paper proposes a tensor-based interpolation method to…

We extend the twin-space formulation of the hierarchical equations of motion approach in combination with the matrix product state representation (introduced in J. Chem. Phys. 150, 234102, [2019]) to nonequilibrium scenarios where the open…