Related papers: Matrix Product States for dynamical simulation of …
A promising application of neural-network quantum states is to describe the time dynamics of many-body quantum systems. To realize this idea, we employ neural-network quantum states to approximate the implicit midpoint rule method, which…
We present a fully automated method that identifies attractors and their basins of attraction without approximations of the dynamics. The method works by defining a finite state machine on top of the system flow. The input to the method is…
We describe an algorithm to simulate time evolution using the Multi-scale Entanglement Renormalization Ansatz (MERA) and test it by studying a critical Ising chain with periodic boundary conditions and with up to L ~ 10^6 quantum spins. The…
We consider the full probability distribution for the transverse magnetization of a finite subsystem in the transverse field Ising chain. We derive a determinant representation of the corresponding characteristic function for general…
We study quantum phase transitions by measuring the bond energy, the number density, and the half-chain entanglement entropy in the one-dimensional ionic Hubbard model. By performing the infinite density matrix renormalization group with…
In this work, we consider the imaginary time evolution of matrix product states. We present a novel quantum-inspired classical method that, when combined with time evolving block decimation (TEBD), is able to potentially speed-up the…
Using the matrix product formalism, we introduce a two parameter family of exactly solvable $xyz$ spin 1/2 Heisenberg chains in magnetic field (with nearest neighbor interactions) and calculate the ground state and correlation functions in…
By removing one empty site between two occupied sites, we map the ground states of chains of hardcore bosons and spinless fermions with infinite nearest-neighbor repulsion to ground states of chains of hardcore bosons and spinless fermions…
Using finite difference method, time evolution of a typical metal molecule metal system is studied by introducing a new method to solve general related Volterra integro differential equation (IDE). Discretization in time domain is applied…
We show that any matrix product state (MPS) can be exactly represented by a recurrent neural network (RNN) with a linear memory update. We generalize this RNN architecture to 2D lattices using a multilinear memory update. It supports…
Molecular dynamics simulation methods are used to study the folding of polymer chains into packed cubic states. The polymer model, based on a chain of linked sites moving in the continuum, includes both excluded volume and torsional…
Matrix Product States (MPS), also known as Tensor Train (TT) decomposition in mathematics, has been proposed originally for describing an (especially one-dimensional) quantum system, and recently has found applications in various…
Tensor networks are often used to accurately represent ground states of quantum spin chains. Two popular choices of such tensor network representations can be seen to implement linear maps that correspond, respectively, to euclidean time…
Recurrent neural networks are machine learning algorithms which are suited well to predict time series. Echo state networks are one specific implementation of such neural networks that can describe the evolution of dynamical systems by…
We address the problem of identifying the dynamical law governing the evolution of a population of indistinguishable particles, when only aggregate distributions at successive times are observed. Assuming a Markovian evolution on a discrete…
Computation of observables in discrete stochastic, possibly conditioned, dynamics over large sparse networks is at the basis of a myriad of applications. The Matrix-Product Belief Propagation method allows a semi-analytical estimation of…
The entangling power and operator entanglement entropy are state independent measures of entanglement. Their growth and saturation is examined in the time-evolution operator of quantum many-body systems that can range from the integrable to…
In applications of nonlinear and complex dynamical systems, a common situation is that the system can be measured but its structure and the detailed rules of dynamical evolution are unknown. The inverse problem is to determine the system…
We describe a class of spin chains with new physical and computational properties. On the physical side, the spin chains give examples of symmetry-protected topological phases that are defined by non-onsite symmetries, i.e. symmetries that…
Checking infinite-state systems is frequently done by encoding infinite sets of states as regular languages. Computing such a regular representation of, say, the set of reachable states of a system requires acceleration techniques that can…