Related papers: Algorithms for entanglement renormalization
Tensor network states are used to approximate ground states of local Hamiltonians on a lattice in D spatial dimensions. Different types of tensor network states can be seen to generate different geometries. Matrix product states (MPS) in…
Entanglement renormalization is a unitary real-space renormalization scheme. The corresponding quantum circuits or tensor networks are known as MERA, and they are particularly well-suited to describing quantum systems at criticality. In…
A class of restarted randomized surrounding methods are presented to accelerate the surrounding algorithms by restarted techniques for solving the linear equations. Theoretical analysis prove that the proposed method converges under the…
A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed. The algorithm, a variation on the iterative hard thresholding algorithm for low-rank recovery, is designed to…
We introduce an efficient algorithm for reducing bond dimensions in an arbitrary tensor network without changing its geometry. The method is based on a novel, quantitative understanding of local correlations in a network. Together with a…
We investigate integrable 2-dimensional Hamiltonian systems with scalar and vector potentials, admitting second invariants which are linear or quadratic in the momenta. In the case of a linear second invariant, we provide some examples of…
We propose a convex variational approach to compute localized density matrices for both zero temperature and finite temperature cases, by adding an entry-wise $\ell_1$ regularization to the free energy of the quantum system. Based on the…
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)…
Understanding the collective behavior of a quantum many-body system, a system composed of a large number of interacting microscopic degrees of freedom, is a key aspect in many areas of contemporary physics. However, as a direct consequence…
Recently, we showed that optimization problems, both in infinite as well as in finite dimensions, for continuous variables and soft excluded volume constraints, can display entire isostatic phases where local minima of the cost function are…
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…
The typical approach for recovery of spatially correlated signals is regularized least squares with a coupled regularization term. In the Bayesian framework, this algorithm is seen as a maximum-a-posterior estimator whose postulated prior…
The coefficient matrix is an efficient tool in entanglement classification under stochastic local operation and classical communication. In this work, we take all the ranks of the coefficient matrices into account in the method of…
By adding entropic regularization, multi-marginal optimal transport problems can be transformed into tensor scaling problems, which can be solved numerically using the multi-marginal Sinkhorn algorithm. The main computational bottleneck of…
We propose and study an algorithm for computing a nearest passive system to a given non-passive linear time-invariant system (with much freedom in the choice of the metric defining `nearest', which may be restricted to structured…
We propose a hybrid quantum-classical algorithm for approximating the ground state of two-dimensional quantum systems using an isometric tensor network ansatz, which maps naturally to quantum circuits. Inspired by the density matrix…
Based on the results of a recent reexamination of the quantization of systems with first-class and second-class constraints from the point of view of coherent-state phase-space path integration, we give additional examples of the…
We are concerned with the computation of the mean-time-to-absorption (MTTA) for a large system of loosely interconnected components, modeled as continuous time Markov chains. In particular, we show that splitting the local and…
The Metropolis process (MP) and Simulated Annealing (SA) are stochastic local search heuristics that are often used in solving combinatorial optimization problems. Despite significant interest, there are very few theoretical results…
Matrix models of 2d quantum gravity coupled to matter field are investigated by the renormalized perturbational method, in which the matrix model Hamiltonian is represented by the equivalent vector model. By the saddle point method, the…