Related papers: Shortcut Matrix Product States and its application…
For three-dimensional (3D) magnetic objects with linear size $L$ exceeding a few exchange lengths, the micromagnetic state exhibits pronounced informational sparsity: low-dimensional, high-gradient regions (e.g., domain walls) coexist with…
Multilayer perceptrons (MLP), or fully connected artificial neural networks, are known for performing vector-matrix multiplications using learnable weight matrices; however, their practical application in many machine learning tasks,…
This thesis is divided into two mainly independent parts: In the first part, we derive a criterion to determine when a translationally invariant Matrix Product State (MPS) has long range localizable entanglement, which indicates that the…
Matrix Product States (MPS) and Projected Entangled Pair States (PEPS) are powerful analytical and numerical tools to assess quantum many-body systems in one and higher dimensions, respectively. While MPS are comprehensively understood, in…
Preparing matrix product states (MPSs) on quantum computers is an essential routine in the simulation of many-body physics. However, widely-used schemes based on staircase circuits are often too deep to execute on current hardware. Here we…
Continuous Matrix Product States (cMPS) are powerful variational ansatz states for ground states of continuous quantum field theories in (1+1) dimension. In this paper we introduce a novel parametrization of the cMPS wave function based on…
High-dimensional token embeddings underpin Large Language Models (LLMs), as they can capture subtle semantic information and significantly enhance the modelling of complex language patterns. However, this high dimensionality also introduces…
Despite the promising performance of state space models (SSMs) in long sequence modeling, limitations still exist. Advanced SSMs like S5 and S6 (Mamba) in addressing non-uniform sampling, their recursive structures impede efficient SSM…
Matrix product states (MPS) are a standard tensor-network representation for ground states of one-dimensional quantum many-body systems, and they underpin widely used simulation tools such as DMRG. However, while quantum model checking has…
By combining the continuous matrix product state (cMPS) representation for quantum fields in the continuum with standard optimization techniques for matrix product states (MPS) on the lattice, we obtain an approximation $|\Psi\rangle$,…
Kinetic simulations of collisionless (or weakly collisional) plasmas using the Vlasov equation are often infeasible due to high resolution requirements and the exponential scaling of computational cost with respect to dimension. Recently,…
Tensor networks establish an adaptable framework for the emulation of quantum circuits. By partitioning exponentially large registers and gates into smaller tensors, this unlocks fast transformations through tensor algebra, and grants fine…
The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional function approximations arising from computational and data sciences. Various sequential and parallel TT decomposition algorithms have…
The advancement of quantum simulators motivates the development of a theoretical framework to assist with efficient state preparation in quantum many-body systems. Generally, preparing a target entangled state via unitary evolution with…
We introduce a method based on matrix product states (MPS) for computing spectral functions of (quasi) one-dimensional spin chains, working directly in momentum space in the thermodynamic limit. We simulate the time evolution after applying…
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…
We introduce an efficient method to calculate the ground state of one-dimensional lattice models with periodic boundary conditions. The method works in the representation of Matrix Product States (MPS), related to the Density Matrix…
A matrix product state formulation of the multiconfiguration time-dependent Hartree (MPS-MCTDH) theory is presented. The Hilbert space that is spanned by the direct products of the phonon degree of freedoms, which is linearly parameterized…
Just as matrix product states represent ground states of one-dimensional quantum spin systems faithfully, continuous matrix product states (cMPS) provide faithful representations of the vacuum of interacting field theories in one spatial…
Modeling the joint distribution of high-dimensional data is a central task in unsupervised machine learning. In recent years, many interests have been attracted to developing learning models based on tensor networks, which have the…