Related papers: Fast convergence of imaginary time evolution tenso…

We address the problem of accelerating thin-shell deformable object simulations by dimension reduction. We present a new algorithm to embed a high-dimensional configuration space of deformable objects in a low-dimensional feature space,…

Topological order in a 2d quantum matter can be determined by the topological contribution to the entanglement R\'enyi entropies. However, when close to a quantum phase transition, its calculation becomes cumbersome. Here we show how…

We develop the theory of Energy Conserving Descent (ECD) and introduce ECDSep, a gradient-based optimization algorithm able to tackle convex and non-convex optimization problems. The method is based on the novel ECD framework of…

Simulating many-body quantum systems on a classical computer is difficult due to the large number of degrees of freedom, causing the computational complexity to grow exponentially with system size. Tensor Networks (TN) is a framework that…

Simulating the time evolution of Partial Differential Equations (PDEs) of large-scale systems is crucial in many scientific and engineering domains such as fluid dynamics, weather forecasting and their inverse optimization problems.…

Tensor permutation is a fundamental operation widely applied in AI, tensor networks, and related fields. However, it is extremely complex, and different shapes and permutation maps can make a huge difference. SIMD permutation began to be…

Tensor network algorithms can efficiently simulate complex quantum many-body systems by utilizing knowledge of their structure and entanglement. These methodologies have been adapted recently for solving the Navier-Stokes equations, which…

Time-delay embedding is a powerful technique for reconstructing the state space of nonlinear time series. However, the fidelity of reconstruction relies on the assumption that the time-delay map is an embedding, which is implicitly…

Tensor networks are often used to accurately represent ground states of quantum spin chains. Two popular choices of such tensor network representations can be seen to implement linear maps that correspond, respectively, to euclidean time…

Navigating densely vegetated environments poses significant challenges for autonomous ground vehicles. Learning-based systems typically use prior and in-situ data to predict terrain traversability but often degrade in performance when…

A projected entangled pair state (PEPS) with ancillas can be evolved in imaginary time to obtain thermal states of a strongly correlated quantum system on a 2D lattice. Every application of a Suzuki-Trotter gate multiplies the PEPS bond…

A novel energy-efficient edge computing paradigm is proposed for real-time deep learning-based image upsampling applications. State-of-the-art deep learning solutions for image upsampling are currently trained using either resize or…

Optimizing tensor networks with standard first-order methods often leads to slow convergence and entrapment in local minima. Although second-order optimization offers enhanced robustness, explicitly constructing the full Hessian matrix is…

The hierarchical equations of motion (HEOM) method is a numerically exact open quantum system dynamics approach. The method is rooted in an exponential expansion of the bath correlation function, which in essence strategically reshapes a…

We use TensorNetwork [C. Roberts et al., arXiv: 1905.01330], a recently developed API for performing tensor network contractions using accelerated backends such as TensorFlow, to implement an optimization algorithm for the Multi-scale…

The Hubbard model has occupied the minds of condensed matter physicists for most part of the last century. This model provides insight into a range of phenomena in correlated electron systems. We wish to examine the paradigm of quantum…

Many recent tensor network algorithms apply unitary operators to parts of a tensor network in order to reduce entanglement. However, many of the previously used iterative algorithms to minimize entanglement can be slow. We introduce an…

Many-body quantum systems are subjected to the Curse of Dimensionality: The dimension of the Hilbert space $\mathcal{H}$, where these systems live in, grows exponentially with systems' 'size' (number of their components, "bodies"). It means…

Tree tensor network (TTN) provides an essential theoretical framework for the practical simulation of quantum many-body systems, where the network structure defined by the connectivity of the isometry tensors plays a crucial role in…

Tensor networks provide a useful tool to describe low-dimensional complex many-body systems. Finding efficient algorithms to use these methods for finite-temperature simulations in two dimensions is a continuing challenge. Here, we use the…