Related papers: Simulating quantum dynamics in two-dimensional lat…
We have proposed an efficient algorithm to calculate physical quantities in the translational invariant three-dimensional tensor networks, which is particularly relevant to the study of the three-dimensional classical statistical models and…
We approach the 3-SAT satisfiability problem with the quantum-inspired method of imaginary time propagation (ITP) applied to matrix product states (MPS) on a classical computer. This ansatz is fundamentally limited by a quantum entanglement…
We first present an empirical study of the Belief Propagation (BP) algorithm, when run on the random field Ising model defined on random regular graphs in the zero temperature limit. We introduce the notion of maximal solutions for the BP…
We propose a new algorithm for inferring the state of hidden spins and reconstructing the connections in a synchronous kinetic Ising model, given the observed history. Focusing on the case in which the hidden spins are conditionally…
Belief Propagation is a well-studied message-passing algorithm that runs over graphical models and can be used for approximate inference and approximation of local marginals. The resulting approximations are equivalent to the Bethe-Peierls…
We introduce a numerical approach to calculate the statistics of work done on 1D quantum lattice systems initially prepared in thermal equilibrium states. This approach is based on two tensor-network techniques: Time Evolving Block…
In the context of inference with expectation constraints, we propose an approach based on the "loopy belief propagation" algorithm LBP, as a surrogate to an exact Markov Random Field MRF modelling. A prior information composed of…
Describing dynamics of quantum many-body systems is a formidable challenge due to rapid generation of quantum entanglement between remote degrees of freedom. A promising approach to tackle this challenge, which has been proposed recently,…
Based on the tensor network state representation, we develop a nonlinear dynamic theory coined as network contractor dynamics (NCD) to explore the thermodynamic properties of two-dimensional quantum lattice models. By invoking the rank-$1$…
Belief propagation (BP) can be a useful tool to approximately contract a tensor network, provided that the contributions from any closed loops in the network are sufficiently weak. In this manuscript we describe how a loop series expansion…
When studying interacting systems, computing their statistical properties is a fundamental problem in various fields such as physics, applied mathematics, and machine learning. However, this task can be quite challenging due to the…
Nuclear quantum effects and non-Born--Oppenheimer effects play a vital role in many chemical and biological processes, motivating the incorporation of such effects into dynamical simulations. In real-time nuclear--electronic orbital…
The time evolution of the entanglement entropy in non-equilibrium quantum systems provides crucial information about the structure of the time-dependent state. For quantum quench protocols, by combining a quasiparticle picture for the…
Representation learning on static graph-structured data has shown a significant impact on many real-world applications. However, less attention has been paid to the evolving nature of temporal networks, in which the edges are often changing…
We investigate the computational power of the recently introduced class of isometric tensor network states (isoTNSs), which generalizes the isometric conditions of the canonical form of one-dimensional matrix-product states to tensor…
Belief Propagation (BP) is an important message-passing algorithm for various reasoning tasks over graphical models, including solving the Constraint Optimization Problems (COPs). It has been shown that BP can achieve state-of-the-art…
The rapid growth of entanglement under unitary time evolution is the primary bottleneck for modern tensor-network techniques--such as Matrix Product States (MPS)--when computing time-dependent expectation values. This {entanglement barrier}…
The $1+1$ dimensional $Z_2$ gauge theory is the simplest model that allows for quantum computation or quantum simulation to probe the fundamental aspects of a gauge theory coupled with dynamical fermions. To reliably benchmark such a…
This work explores the use of a tree tensor network ansatz to simulate the ground state of a local Hamiltonian on a two-dimensional lattice. By exploiting the entropic area law, the tree tensor network ansatz seems to produce quasi-exact…
The quantum dynamics of many-qubit systems is an outstanding problem that has recently driven significant advances in both numerical methods and programmable quantum processing units. In this work, we employ a comprehensive toolbox of…