Related papers: Exploiting the Hermitian symmetry in tensor networ…
The benefits of exploiting the presence of symmetries in tensor network algorithms have been extensively demonstrated in the context of matrix product states (MPSs). These include the ability to select a specific symmetry sector (e.g. with…
Due to the unfavorable scaling of tensor network methods with the refinement parameter M, new approaches are necessary to improve the efficiency of numerical simulations based on such states in particular for gapless, strongly entangled…
Symmetric tensor operations arise in a wide variety of computations. However, the benefits of exploiting symmetry in order to reduce storage and computation is in conflict with a desire to simplify memory access patterns. In this paper, we…
This paper is a manual with tips and tricks for programming tensor network algorithms with global $SU(2)$ symmetry. We focus on practical details that are many times overlooked when it comes to implementing the basic building blocks of…
In this thesis we extend the formalism of tensor network algorithms to incorporate global internal symmetries. We describe how to both numerically protect the symmetry and exploit it for computational gain in tensor network simulations. Our…
Simulation of quantum systems is challenging due to the exponential size of the state space. Tensor networks provide a systematically improvable approximation for quantum states. 2D tensor networks such as Projected Entangled Pair States…
Projected entangled-pair states (PEPS) have become a powerful tool for studying quantum many-body systems in the condensed matter and quantum materials context, particularly with advances in variational energy optimization methods. A key…
We show how fermionic statistics can be naturally incorporated in tensor networks on arbitrary graphs through the use of graded Hilbert spaces. This formalism allows to use tensor network methods for fermionic lattice systems in a local…
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…
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 networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to…
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. We discuss how to incorporate a global symmetry, given by a…
Infinite projected entangled-pair states (iPEPS) provide a powerful tool for studying strongly correlated systems directly in the thermodynamic limit. A core component of the algorithm is the approximate contraction of the iPEPS, where the…
We are upgrading the Python-version of RTNI, which symbolically integrates tensor networks over the Haar-distributed unitary matrices. Now, PyRTNI2 can treat the Haar-distributed orthogonal matrices and the real and complex normal Gaussian…
The 1-form symmetry, manifesting as loop-like symmetries, has gained prominence in the study of quantum phases, deepening our understanding of symmetry. However, the role of 1-form symmetries in Projected Entangled-Pair States (PEPS),…
A tensor network renormalization algorithm with global optimization based on the corner transfer matrix is proposed. Since the environment is updated by the corner transfer matrix renormalization group method, the forward-backward iteration…
Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…
This is a short review on selected theory developments on Tensor Network (TN) states for strongly correlated systems. Specifically, we briefly review the effect of symmetries in TN states, fermionic TNs, the calculation of entanglement…
Tensor networks are a very powerful data structure tool originating from quantum system simulations. In recent years, they have seen increased use in machine learning, mostly in trainings with gradient-based techniques, due to their…
Improving the computational efficiency of quantum many-body calculations from a hardware perspective remains a critical challenge. Although field-programmable gate arrays (FPGAs) have recently been exploited to improve the computational…