相关论文: Chebyshev pseudosite matrix product state approach…

Optimization problems with constraints in the form of a partial differential equation arise frequently in the process of engineering design. The discretization of PDE-constrained optimization problems results in large-scale linear systems…

Infinite projected entangled-pair states (iPEPS) provide a powerful variational framework for two-dimensional quantum matter and have been widely used to capture bosonic topological order, including chiral spin liquids. Here we extend this…

Studying finite-temperature properties with tensor networks is notoriously difficult, especially at low temperatures, due to the rapid growth of entanglement and the complexity of thermal states. Existing methods like purification and…

We extend the recently introduced continuous matrix product state (cMPS) variational class to the setting of (1+1)-dimensional relativistic quantum field theories. This allows one to overcome the difficulties highlighted by Feynman…

We study Chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices. In this technique the subspace projection onto the target space of wanted eigenvectors is…

We present second-order molecular cluster perturbation theory (MCPT(2)), a linear scaling methodology to calculate arbitrarily large systems with explicit calculation of individual wavefunctions in a coupled-cluster framework. This new…

Problems of finite-temperature quantum statistical mechanics can be formulated in terms of imaginary (Euclidean) -time Green's functions and self-energies. In the context of realistic Hamiltonians, the large energy scale of the Hamiltonian…

We present an excited-state-specific coupled-cluster approach in which both the molecular orbitals and cluster amplitudes are optimized for an individual excited state. The theory is formulated via a pseudoprojection of the traditional…

We present an adaptive Finite State Projection (FSP) method for efficiently solving the Chemical Master Equation (CME) with rigorous error control. Our approach integrates time-stepping with dynamic state-space truncation, balancing…

This work develops novel strategies for optimal planning with semantic observations using continuous state partially observable markov decision processes (CPOMDPs). Two major innovations are presented in relation to Gaussian mixture (GM)…

It is known that the statistical properties of the spectrum provide an essential characterization of quantum chaos. The computation of a large group of interior eigenvalues at the middle spectrum is thus an important problem for quantum…

The chemical master equation (CME) is frequently used in systems biology to quantify the effects of stochastic fluctuations that arise due to biomolecular species with low copy numbers. The CME is a system of ordinary differential equations…

Performing model selection for coupled hidden Markov models (CHMMs) is highly challenging, owing to the large dimension of the hidden state process. Whilst in principle the hidden state process can be marginalized out via forward filtering,…

Semi-empirical quantum models such as Density Functional Tight Binding (DFTB) are attractive methods for obtaining quantum simulation data at longer time and length scales than possible with standard approaches. However, application of…

Correlator product states (CPS) are a class of tensor network wavefunctions applicable to strongly correlated problems in arbitrary dimensions. Here, we present a method for optimizing and evaluating the energy of the CPS wavefunction that…

Chiral Spin Liquids (CSL) based on spin-1/2 fermionic Projected Entangled Pair States (fPEPS) are considered on the square lattice. First, fPEPS approximants of Gutzwiller-projected Chern insulators (GPCI) are investigated by Variational…

The density-matrix renormalization group method has become a standard computational approach to the low-energy physics as well as dynamics of low-dimensional quantum systems. In this paper, we present a new set of applications, available as…

Numerical simulations are a powerful tool to study quantum systems beyond exactly solvable systems lacking an analytic expression. For one-dimensional entangled quantum systems, tensor network methods, amongst them Matrix Product States…

The cluster perturbation theory (CPT) is one of the simplest but systematic quantum cluster approaches to lattice models of strongly correlated electrons with local interactions. By treating the inter-cluster potential, in addition to the…

We show that infinite Matrix Product States (MPS) constructed from conformal field theories can describe ground states of one-dimensional critical systems with open boundary conditions. To illustrate this, we consider a simple infinite MPS…