Related papers: Improved real-space parallelizable matrix-product …
The curse of dimensionality is ubiquitous in both numerical and data-driven methods. This is particularly severe for space-time methods, which treat the combined space-time domain simultaneously. We investigate the effectiveness of a…
A large, or even infinite, local Hilbert space dimension poses a significant computational challenge for simulating quantum systems. In this work, we present a matrix product state (MPS)-based method for simulating one-dimensional quantum…
An algorithm for the simulation of the evolution of slightly entangled quantum states has been recently proposed as a tool to study time-dependent phenomena in one-dimensional quantum systems. Its key feature is a time-evolving…
Recent work by Wu {\em et al.} [arXiv:1910.11011] proposed a numerical method, so-called matrix product operator-matrix product state (MPO-MPS) method, by which several types of quantum many-body wave functions, in particular, the projected…
We introduce AQCtensor, a novel algorithm to produce short-depth quantum circuits from Matrix Product States (MPS). Our approach is specifically tailored to the preparation of quantum states generated from the time evolution of quantum…
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…
Static disorder plays a crucial role in the electronic dynamics and spectroscopy of complex molecular systems. Traditionally, obtaining observables averaged over static disorder requires thousands of realizations via direct sampling of the…
Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular case of TNS and are used for the simulation of 1+1 dimensional…
Compressed sensing is a method that allows a significant reduction in the number of samples required for accurate measurements in many applications in experimental sciences and engineering. In this work, we show that compressed sensing can…
We show how to simulate numerically both the evolution of 1D quantum systems under dissipation as well as in thermal equilibrium. The method applies to both finite and inhomogeneous systems and it is based on two ideas: (a) a representation…
A generic method to investigate many-body continuous-variable systems is pedagogically presented. It is based on the notion of matrix product states (so-called MPS) and the algorithms thereof. The method is quite versatile and can be…
Matrix product states (MPS) and matrix product operators (MPOs) are one dimensional tensor networks that underlie the modern density matrix renormalization group (DMRG) algorithm. The use of MPOs accounts for the high level of generality…
A key challenge for quantum computers is the efficient preparation of many-body entangled states across many qubits. In this work, we demonstrate the preparation of matrix product states (MPS) using a renormalization-group(RG)-based quantum…
We investigate the use of matrix product states (MPS) to approximate ground states of critical quantum spin chains with periodic boundary conditions (PBC). We identify two regimes in the (N,D) parameter plane, where N is the size of the…
Sampling problems have emerged as a central avenue for demonstrating quantum advantage on noisy intermediate-scale quantum devices. However, physical noise can fundamentally alter their computational complexity, often making them…
The continuous matrix product state (cMPS) ansatz is a promising numerical tool for studying quantum many-body systems in continuous space. Although it provides a clean framework that allows one to directly simulate continuous systems, the…
We present the AMPS algorithm, a finite element solution method that combines principal submatrix updates and Schur complement techniques, well-suited for interactive simulations of deformation and cutting of finite element meshes. Our…
The dynamics of one-dimensional quantum many-body systems is often numerically simulated with matrix-product states (MPSs). The computational complexity of MPS methods is known to be related to the growth of entropies of reduced density…
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…
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…