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We are on the verge of a revolutionary era in space exploration, thanks to advancements in telescopes such as the James Webb Space Telescope (\textit{JWST}). High-resolution, high signal-to-noise spectra from exoplanet and brown dwarf…
This work is devoted to the study Translation-Invariant (TI) Matrix Product State (MPS) representations of quantum states with periodic boundary conditions (PBC). We pursue two directions: we introduce new methods for constructing TI MPS…
Finance, especially option pricing, is a promising industrial field that might benefit from quantum computing. While quantum algorithms for option pricing have been proposed, it is desired to devise more efficient implementations of costly…
Distributed, large-scale quantum computing will need architectures that combine matter-based qubits with photonic links, but today's software stacks target either gate-based chips or linear-optical devices in isolation. We introduce Optyx,…
In this technical paper we introduce the Tensor Network Theory (TNT) library -- an open-source software project aimed at providing a platform for rapidly developing robust, easy to use and highly optimised code for TNT calculations. The…
This paper introduces matrix product state (MPS) decomposition as a computational tool for extracting features of multidimensional data represented by higher-order tensors. Regardless of tensor order, MPS extracts its relevant features to…
Tensor Networks are non-trivial representations of high-dimensional tensors, originally designed to describe quantum many-body systems. We show that Tensor Networks are ideal vehicles to connect quantum mechanical concepts to machine…
Mean-field theories have proven to be efficient tools for exploring diverse phases of matter, complementing alternative methods that are more precise but also more computationally demanding. Conventional mean-field theories often fall short…
Generation and analysis of time-series data is relevant to many quantitative fields ranging from economics to fluid mechanics. In the physical sciences, structures such as metastable and coherent sets, slow relaxation processes, collective…
We propose a new version of the matrix product (MP) states approach to the description of quantum spin chains, which allows one to construct MP states with certain total spin and its z-projection. We show that previously known MP…
We describe a class of neuralized fermionic tensor network states (NN-fTNS) that introduce non-linearity into fermionic tensor networks through configuration-dependent neural network transformations of the local tensors. The construction…
In this work, we present a novel representation of matrix product states (MPS) within the framework of quasi-local algebras. By introducing an enhanced compatibility condition, we enable the extension of finite MPS to an infinite-volume…
The mean field algorithm is a widely used approximate inference algorithm for graphical models whose exact inference is intractable. In each iteration of mean field, the approximate marginals for each variable are updated by getting…
The Python package pylimer-tools is a comprehensive toolkit for computational studies of polymer networks, particularly bead-spring networks. The package provides functionality to generate polymer networks using Monte Carlo (MC) procedures…
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 $|\Psi\rangle$,…
In recent years, a close connection between the description of open quantum systems, the input-output formalism of quantum optics, and continuous matrix product states in quantum field theory has been established. So far, however, this…
We present some exact results for the optimal Matrix Product State (MPS) approximation to the ground state of the infinite isotropic Heisenberg spin-1/2 chain. Our approach is based on the systematic use of Schmidt decompositions to reduce…
Tensor networks such as matrix product states (MPS) and projected entangled pair states (PEPS) are commonly used to approximate quantum systems. These networks are optimized in methods such as DMRG or evolved by local operators. We provide…
In this paper we construct the continuous Matrix Product State (MPS) representation of the vacuum of the field theory corresponding to the continuous limit of an Ising model. We do this by exploiting the observation made by Hastings and…
In stochastic modeling, there has been a significant effort towards finding predictive models that predict a stochastic process' future using minimal information from its past. Meanwhile, in condensed matter physics, matrix product states…