Related papers: Efficient optimization of variational tensor-netwo…
We introduce a variational Monte Carlo algorithm for approximating finite-temperature quantum many-body systems, based on the minimization of a modified free energy. This approach directly approximates the state at a fixed temperature,…
Tensor network methods are powerful tools for studying quantum many-body systems. In this paper, we investigate the emergent statistical properties of random high-dimensional tensor-network states and the trainability of variational tensor…
Markov chain Monte Carlo (MCMC) is a powerful tool for sampling from complex probability distributions. Despite its versatility, MCMC often suffers from strong autocorrelation and the negative sign problem, leading to slowing down the…
We investigate the Kramers-Wannier approximation for the three-dimensional (3D) Ising model. The variational state is represented by an effective 2D Ising model, which contains two variational parameters. We numerically calculate the…
Tensor Networks (TN) are approximations of high-dimensional tensors designed to represent locally entangled quantum many-body systems efficiently. This study provides a comprehensive comparison between classical TNs and TN-inspired quantum…
We present new results on the classical algorithm of variable elimination, which underlies many algorithms including for probabilistic inference. The results relate to exploiting functional dependencies, allowing one to perform inference…
Tensor networks provide a useful tool to describe low-dimensional complex many-body systems. Finding efficient algorithms to use these methods for finite-temperature simulations in two dimensions is a continuing challenge. Here, we use the…
We introduce a Metropolis-Hastings Markov chain for Boltzmann distributions of classical spin systems. It relies on approximate tensor network contractions to propose correlated collective updates at each step of the evolution. We present…
Tensor networks are a class of algorithms aimed at reducing the computational complexity of high-dimensional problems. They are used in an increasing number of applications, from quantum simulations to machine learning. Exploiting data…
Quantum computers are expected to enable fast solving of large-scale combinatorial optimization problems. However, their limitations in fidelity and the number of qubits prevent them from handling real-world problems. Recently, a…
In recent advances in solving the problem of transmission network expansion planning, the use of robust optimization techniques has been put forward, as an alternative to stochastic mathematical programming methods, to make the problem…
We introduce a numerical method to study critical properties near classical and quantum phase transitions. Our method applies ideas of the Tensor Renormalization Group to obtain an improved action which is used to extract critical…
The study of quantum circuit simulation using classical computers is a key research topic that helps define the boundary of verifiable quantum advantage, solve quantum many-body problems, and inform development of quantum hardware and…
We present a new method for online prediction and learning of tensors ($N$-way arrays, $N >2$) from sequential measurements. We focus on the specific case of 3-D tensors and exploit a recently developed framework of structured tensor…
We propose a tensor-network-based algorithm to study the classical Ising model on an infinitely large hyperbolic lattice with a regular 3D tesselation of identical dodecahedra. We reformulate the corner transfer matrix renormalization group…
A Gibbs operator $e^{-\beta H}$ for a 2D lattice system with a Hamiltonian $H$ can be represented by a 3D tensor network, the third dimension being the imaginary time (inverse temperature) $\beta$. Coarse-graining the network along $\beta$…
Tensor network states are powerful variational ans\"atze for many-body ground states of quantum lattice models. The use of Monte Carlo sampling techniques in tensor network approaches significantly reduces the cost of tensor contractions,…
Multivariate time series prediction has applications in a wide variety of domains and is considered to be a very challenging task, especially when the variables have correlations and exhibit complex temporal patterns, such as seasonality…
A novel algorithm based on the optimized decimation of tensor networks with super-orthogonalization (ODTNS) that can be applied to simulate efficiently and accurately not only the thermodynamic but also the ground state properties of…
We present a new algorithm for recovering paths from their third-order signature tensors, an inverse problem in rough analysis. Our algorithm provides the exact solution to this learning problem and improves upon current approaches by an…