Related papers: Overcoming the entanglement barrier with sampled t…
Simulating quantum systems constructively furthers our understanding of qualitative and quantitative features which may be analytically intractable. In this letter, we directly simulate and explore the entanglement structure present in a…
The efficient simulation of complex quantum systems remains a central challenge due to the exponential growth of Hilbert space with system size. Tensor network methods have long been established as powerful approximation schemes, and their…
Quantum processing units boost entanglement at the level of hardware and enable physical simulations of highly correlated electron states in molecules and intermolecular chemical bonds. The variational quantum eigensolver provides a…
Tensor network (TN) methods are well established for computing partition functions in statistical mechanics, though this use has traditionally been limited to lattice models. We extend the scope of TN methodology to interacting particle…
We propose an approach to study the ground state of quantum many-body systems in which Tensor Network States (TNS), specifically Projected Entangled Pair States (PEPS), and Green's function Monte Carlo (GFMC) are combined. PEPS, by design,…
Many problems of practical interest rely on Continuous-time Markov chains~(CTMCs) defined over combinatorial state spaces, rendering the computation of transition probabilities, and hence probabilistic inference, difficult or impossible…
We present a numerical strategy to efficiently estimate bipartite entanglement measures, and in particular the Entanglement of Formation, for many-body quantum systems on a lattice. Our approach exploits the Tree Tensor Operator tensor…
In this article we propose a novel MCMC method based on deterministic transformations T: X x D --> X where X is the state-space and D is some set which may or may not be a subset of X. We refer to our new methodology as Transformation-based…
Optimizing or sampling complex cost functions of combinatorial optimization problems is a longstanding challenge across disciplines and applications. When employing family of conventional algorithms based on Markov Chain Monte Carlo (MCMC)…
Entanglement forging based variational algorithms leverage the bi-partition of quantum systems for addressing ground state problems. The primary limitation of these approaches lies in the exponential summation required over the numerous…
We present a statistical framework for extracting spatially resolved entanglement directly from an ensemble of marginal (one-body) wavefunctions in Time-Dependent Quantum Monte Carlo (TDQMC). Treating the guide waves as a statistical…
In this paper, we present the construction of tensor network states (TNS) for some of the degenerate ground states of 3D stabilizer codes. We then use the TNS formalism to obtain the entanglement spectrum and entropy of these ground-states…
Recent works put much effort into tensor network structure search (TN-SS), aiming to select suitable tensor network (TN) structures, involving the TN-ranks, formats, and so on, for the decomposition or learning tasks. In this paper, we…
The recognition that large classes of quantum many-body systems have limited entanglement in the ground and low-lying excited states led to dramatic advances in their numerical simulation via so-called tensor networks. However, global…
Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…
Reliably simulating two-dimensional many-body quantum dynamics with projected entangled pair states (PEPS) has long been a difficult challenge. In this work, we overcome this barrier for low-energy quantum dynamics by developing a stable…
Chaotic time series forecasting has been far less understood despite its tremendous potential in theory and real-world applications. Traditional statistical/ML methods are inefficient to capture chaos in nonlinear dynamical systems,…
In recent years, the time-dependent variational principle (TDVP) method based on the matrix product state (MPS) wave function formulation has shown its great power in performing large-scale quantum dynamics simulations for realistic…
We establish tight connections between entanglement entropy and the approximation error in Trotter-Suzuki product formulas for Hamiltonian simulation. Product formulas remain the workhorse of quantum simulation on near-term devices, yet…
The success of deep convolutional neural network (CNN) in computer vision especially image classification problems requests a new information theory for function of image, instead of image itself. In this article, after establishing a deep…