Related papers: Optimization schemes for unitary tensor-network ci…
We introduce a new coarse-graining algorithm, tensor network skeletonization, for the numerical computation of tensor networks. This approach utilizes a structure-preserving skeletonization procedure to remove short-range correlations…
We investigate the application of hybrid quantum tensor networks to aeroelastic problems, harnessing the power of Quantum Machine Learning (QML). By combining tensor networks with variational quantum circuits, we demonstrate the potential…
Regularized factorization is proposed to simulate time evolution for quantum lattice systems. Transcending the Trotter decomposition, the resulting compact structure of the propagator indicates a high-order Baker-Campbell-Hausdorff series.…
This paper demonstrates a method for tensorizing neural networks based upon an efficient way of approximating scale invariant quantum states, the Multi-scale Entanglement Renormalization Ansatz (MERA). We employ MERA as a replacement for…
Squared tensor networks (TNs) and their extension as computational graphs--squared circuits--have been used as expressive distribution estimators, yet supporting closed-form marginalization. However, the squaring operation introduces…
Quantum Computing (QC) stands to revolutionize computing, but is currently still limited. To develop and test quantum algorithms today, quantum circuits are often simulated on classical computers. Simulating a complex quantum circuit…
Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. In a recent paper [arXiv:0907.2994v1] we discussed how to…
Tensor network methods are incredibly effective for simulating quantum circuits. This is due to their ability to efficiently represent and manipulate the wave-functions of large interacting quantum systems. We describe the challenges faced…
Understanding the limiting capabilities of classical methods in simulating complex quantum systems is of paramount importance for quantum technologies. Although many advanced approaches have been proposed and recently used to challenge…
In this work, we develop an optimization framework for problems whose solutions are well-approximated by Hierarchical Tucker (HT) tensors, an efficient structured tensor format based on recursive subspace factorizations. By exploiting the…
We propose a simple and generic construction of the variational tensor network operators to study the quantum spin systems by the synergy of ideas from the imaginary-time evolution and variational optimization of trial wave functions. By…
Novel randomness-induced disordered ground states in two-dimensional (2D) quantum spin systems have been attracting much interest. For quantitative analysis of such random quantum spin systems, one of the most promising numerical approaches…
We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network…
Quantum computers are expected to enable fast solving of large-scale combinatorial optimization problems. However, their limitations in fidelity and the number of qubits prevent them from handling real-world problems. Recently, a…
We investigate the disordered spin-$\frac12$Heisenberg model in two dimensions and employ tree tensor networks (TTNs) with a physics-informed structural optimization of the tree layout, to simulate dynamics in the many-body localization…
Variational quantum algorithms are a promising class of algorithms that can be performed on currently available quantum computers. In most settings, the free parameters of a variational circuit are optimized using a classical optimizer that…
We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a…
Deep learning is one of the most successful and far-reaching strategies used in machine learning today. However, the scale and utility of neural networks is still greatly limited by the current hardware used to train them. These concerns…
Variational methods have proven to be excellent tools to approximate ground states of complex many body Hamiltonians. Generic tools like neural networks are extremely powerful, but their parameters are not necessarily physically motivated.…
Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…