Related papers: Splitting the local Hilbert space: MPS-based appro…
The constraint coordinate-momentum \textit{phase space} (CPS) has recently been developed to study nonadiabatic dynamics in gas-phase and condensed-phase molecular systems. Although the CPS formulation is exact for describing the discrete…
Many biological and physical systems exhibit behaviour at multiple spatial, temporal or population scales. Multiscale processes provide challenges when they are to be simulated using numerical techniques. While coarser methods such as…
This article presents numerical recipes for simulating high-temperature and non-equilibrium quantum spin systems that are continuously measured and controlled. The notion of a spin system is broadly conceived, in order to encompass…
All simulation approaches eventually face limits in computational scalability when applied to large spatiotemporal domains. This challenge becomes especially apparent in molecular-level particle simulations, where high spatial and temporal…
Matrix product density operators (MPDOs) are tensor network representations of locally purified density matrices where each physical degree of freedom is associated to an environment degree of freedom. MPDOs have interesting properties for…
We present a holographic quantum simulation algorithm to variationally prepare thermal states of $d$-dimensional interacting quantum many-body systems, using only enough hardware qubits to represent a ($d$-1)-dimensional cross-section. This…
We show that the model wave functions used to describe the fractional quantum Hall effect have exact representations as matrix product states (MPS). These MPS can be implemented numerically in the orbital basis of both finite and infinite…
Spin-boson (SB) model plays a central role in studies of dissipative quantum dynamics, both due its conceptual importance and relevance to a number of physical systems. Here we provide rigorous bounds of the computational complexity of the…
We reconstruct a matrix product state (MPS) in reduced spaces using density matrix. This scheme applies to a MPS built on a blocked quantum lattice. Each block contains $N$ physical sites that have a local space of rank $R$. The simulation…
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 $|\Psi\rangle$,…
Recent developments in matrix-product-state (MPS) investigations of many-body localization (MBL) are reviewed, with a discussion of benefits and limitations of the method. This approach allows one to explore the physics around the MBL…
We find an efficient approach to approximately convert matrix product states (MPSs) into restricted Boltzmann machine wave functions consisting of a multinomial hidden unit through a canonical polyadic (CP) decomposition of the MPSs. This…
For a given metric measure space $(X,d,\mu)$ we consider finite samples of points, calculate the matrix of distances between them and then reconstruct the points in some finite-dimensional space using the multidimensional scaling (MDS)…
An efficient numerical method is developed using the matrix product formalism for computing the properties at finite energy densities in one-dimensional (1D) many-body localized (MBL) systems. Arguing that any efficient (possibly quantum)…
Tensor networks, such as matrix product states (MPS) and tree tensor network states (TTNS), are powerful ans\"atze for simulating quantum dynamics. While both ans\"atze are theoretically exact in the limit of large bond dimensions, [J.…
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…
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…
Tensor networks are efficient factorisations of high-dimensional tensors into a network of lower-order tensors. They have been most commonly used to model entanglement in quantum many-body systems and more recently are witnessing increased…
Computing ground states of local Hamiltonians is a fundamental problem in condensed matter physics. We give the first randomized polynomial-time algorithm for finding ground states of gapped one-dimensional Hamiltonians: it outputs an…
Tensor network methods as presented in our open source Matrix Product States software have opened up the possibility to study many-body quantum physics in one and quasi-one-dimensional systems in an easily accessible package similar to…