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Machine learning is a promising application of quantum computing, but challenges remain as near-term devices will have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine…
High-dimensional partial differential equations (PDEs) are ubiquitous in economics, science and engineering. However, their numerical treatment poses formidable challenges since traditional grid-based methods tend to be frustrated by the…
A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the projector onto the tangent space of the tensor manifold. The…
The application of Tensor Networks (TN) in quantum computing has shown promise, particularly for data loading. However, the assumption that data is readily available often renders the integration of TN techniques into Quantum Monte Carlo…
We propose an efficient implementation of the numerical tensor-train (TT) based algorithm solving the multicomponent coagulation equation preserving the nonnegativeness of solution. Unnatural negative elements in the constructed…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
We propose a new method for the efficient approximation of a class of highly oscillatory weighted integrals where the oscillatory function depends on the frequency parameter $\omega \geq 0$, typically varying in a large interval. Our…
The resolution of dynamics in out of equilibrium quantum spin systems lies at the heart of fundamental questions among Quantum Information Processing, Statistical Mechanics and Nano-Technologies. Efficient computational simulations of…
Tensor train (TT) format is a common approach for computationally efficient work with multidimensional arrays, vectors, matrices, and discretized functions in a wide range of applications, including computational mathematics and machine…
Quantum linear system algorithms (QLSAs) for gate-based quantum computing can provide exponential speedups for solving linear systems but face challenges when applied to finite element problems due to the growth of the condition number with…
In this work, we develop a space--time Chebyshev spectral collocation method for three-dimensional Maxwell's equations and combine it with tensor-network techniques in Tensor-Train (TT) format. Under constant material parameters, the…
Real-world physical systems, like composite materials and porous media, exhibit complex heterogeneities and multiscale nature, posing significant computational challenges. Computational homogenization is useful for predicting macroscopic…
Pricing multi-asset options via the Black-Scholes PDE is limited by the curse of dimensionality: classical full-grid solvers scale exponentially in the number of underlyings and are effectively restricted to three assets. Practitioners…
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…
The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional data approximations. In order to represent data with interpretability in data science, researchers develop data-centric skeletonized low…
Simulating nonlinear partial differential equations (PDEs) such as the Navier--Stokes (NS) equations remains computationally intensive, especially when implicit time integration is used to capture multiscale flow dynamics. This work…
We investigate tensor-train approaches to the solution of the time-dependent Schr\"{o}dinger equation for chain-like quantum systems with on-site and nearest-neighbor interactions only. Using efficient low-rank tensor train representations,…
Classical simulation of quantum computation is necessary for studying the numerical behavior of quantum algorithms, as there does not yet exist a large viable quantum computer on which to perform numerical tests. Tensor network (TN)…
We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of…
In this work we investigate replacing standard quadrature techniques used in deterministic linear solvers with a fixed-seed Quasi-Monte Carlo calculation to obtain more accurate and efficient solutions to the neutron transport equation…