Related papers: Chebyshev matrix product state approach for time e…
The simulation of quantum many-body systems poses a significant challenge in physics due to the exponential scaling of Hilbert space with the number of particles. Traditional methods often struggle with large system sizes and frustrated…
To solve the many-boson Schr\"odinger equation we utilize the Multiconfigurational time-dependent Hartree method for bosons (MCTDHB). To be able to attack larger systems and/or to propagate the solution for longer times, we implement a…
We propose a refined matrix product state representation for many-body quantum states that are invariant under SU(2) transformations, and indicate how to extend the time-evolving block decimation (TEBD) algorithm in order to simulate time…
The simulation of quantum systems is a task for which quantum computers are believed to give an exponential speedup as compared to classical ones. While ground states of one-dimensional systems can be efficiently approximated using Matrix…
One of the most fundamental problems in quantum many-body physics is the characterization of correlations among thermal states. Of particular relevance is the thermal area law, which justifies the tensor network approximations to thermal…
Quantum many-body systems involving bosonic modes or gauge fields have infinite-dimensional local Hilbert spaces which must be truncated to perform simulations of real-time dynamics on classical or quantum computers. To analyze the…
We develop the multi-layer multi-configuration time-dependent Hartree method for bosons (ML-MCTDHB), a variational numerically exact ab-initio method for studying the quantum dynamics and stationary properties of bosonic systems. ML-MCTDHB…
Learning the closest matrix product state (MPS) representation of a quantum state enables useful tools for quantum machine learning and analysis of complex quantum systems. In this work, we study the problem of learning MPS in the following…
We develop fast and memory efficient numerical methods for learning functions of many variables that admit sparse representations in terms of general bounded orthonormal tensor product bases. Such functions appear in many applications…
We introduce a novel approach for estimating the spectrum of quantum many-body Hamiltonians, and more generally, of Hermitian operators, using quantum time evolution. In our approach we are evolving a maximally mixed state under the…
Accurate models of the dynamics of quantum circuits are essential for optimizing and advancing quantum devices. Since first-principles models of environmental noise and dissipation in real quantum systems are often unavailable, deriving…
Matrix product states (MPS) have proven to be a very successful tool to study lattice systems with local degrees of freedom such as spins or bosons. Topologically ordered systems can support anyonic particles which are labeled by conserved…
The year 2025 marks the 100 and 30 years anniversaries of the discovery of Bose--Einstein condensation and its successful experimental realisation. Inspired by these important research achievements, a conceptually simple approach is…
This research focuses on solving time-dependent partial differential equations (PDEs), in particular the time-dependent Schr\"odinger equation, using matrix product states (MPS). We propose an extension of Hermite Distributed Approximating…
Following the celebrated quantum algorithm for solving linear equations (so-called HHL algorithm), Childs, Kothari and Somma [SIAM Journal on Computing, {\bf 46}: 1920, (2017)] provided an approach to solve a linear system of equations with…
We present a one-step algorithm that solves the Maxwell equations for systems with spatially varying permittivity and permeability by the Chebyshev method. We demonstrate that this algorithm may be orders of magnitude more efficient than…
Combining the time-dependent variational principle (TDVP) algorithm with the parallelization scheme introduced by Stoudenmire and White for the density matrix renormalization group (DMRG), we present the first parallel matrix product state…
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 projected entangled pair states (PEPS) methods have been proved to be powerful tools to solve the strongly correlated quantum many-body problems in two-dimension. However, due to the high computational scaling with the virtual bond…
We show that recursively generated Chebyshev expansions offer numerically efficient representations for calculating zero-temperature spectral functions of one-dimensional lattice models using matrix product state (MPS) methods. The main…