Related papers: Improving accuracy of tree-tensor network approach…

We analyze the problem of high-order polynomial approximation from a many-body physics perspective, and demonstrate the descriptive power of entanglement entropy in capturing model capacity and task complexity. Instantiated with a…

Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars.…

A novel method has been devised to compute the Local Integrals of Motion (LIOMs) for a one-dimensional many-body localized system. In this approach, a class of optimal unitary transformations is deduced in a tensor-network formalism to…

The contraction cost of a tensor network depends on the contraction order. However, the optimal contraction ordering problem is known to be NP-hard. We show that the linear contraction ordering problem for tree tensor networks admits a…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…

Knowledge embedded in the weights of the artificial neural network can be used to improve the network structure, such as in network compression. However, the knowledge is set up by hand, which may not be very accurate, and relevant…

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…

Tensor networks and quantum computation are two of the most powerful tools for the simulation of quantum many-body systems. Rather than viewing them as competing approaches, here we consider how these two methods can work in tandem. We…

Contracting tensor networks is often computationally demanding. Well-designed contraction sequences can dramatically reduce the contraction cost. We explore the performance of simulated annealing and genetic algorithms, two common discrete…

A novel algorithm based on the optimized decimation of tensor networks with super-orthogonalization (ODTNS) that can be applied to simulate efficiently and accurately not only the thermodynamic but also the ground state properties of…

We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…

The existing randomized algorithms need an initial estimation of the tubal rank to compute a tensor singular value decomposition. This paper proposes a new randomized fixedprecision algorithm which for a given third-order tensor and a…

For successful estimation, the usual network tomography algorithms crucially require i) end-to-end data generated using multicast probe packets, real or emulated, and ii) the network to be a tree rooted at a single sender with destinations…

The numerical simulation of two-dimensional quantum many-body systems away from equilibrium constitutes a major challenge for all known computational methods. We investigate the utility of Tree Tensor Network (TTN) states to solve the…

We study tensor completion (TC) through the lens of low-rank tensor decomposition (TD). Many TD algorithms use fast alternating minimization methods to solve highly structured linear regression problems at each step (e.g., for CP, Tucker,…

Open many-body quantum systems play an important role in quantum optics and condensed-matter physics, and capture phenomena like transport, interplay between Hamiltonian and incoherent dynamics, and topological order generated by…

An augmented tree tensor network (aTTN) is a tensor network ansatz constructed by applying a layer of unitary disentanglers to a tree tensor network. The disentanglers absorb a part of the system's entanglement. This makes aTTNs suitable…

Probabilistic inference is a fundamental task in modern machine learning. Recent advances in tensor network (TN) contraction algorithms have enabled the development of better exact inference methods. However, many common inference tasks in…

In many applications, it is needed to change the topology of a tensor network directly and without approximation. This work will introduce a general scheme that satisfies these needs. We will describe the procedure by two examples and show…

Numerical annealing and renormalization group have conceived various successful approaches to study the thermodynamics of strongly-correlated systems where perturbation or expansion theories fail to work. As the process of lowering the…