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Quantum computing offers the potential for computational abilities that can go beyond classical machines. However, they are still limited by several challenges such as noise, decoherence, and gate errors. As a result, efficient classical…

Quantum Physics · Physics 2025-09-01 Aditya Dubey , Zeki Zeybek , Peter Schmelcher

This work presents a bilevel coordination model that captures the hierarchical interaction between the transmission and distribution layers under a Distribution System Operator(DSO)-led configuration. In this scheme, multiple DSOs…

Optimization and Control · Mathematics 2026-03-25 Fernando García-Muñoz , Martín Venegas Escalona

Tensor train (TT) format is a common approach for computationally efficient work with multidimensional arrays, vectors, matrices, and discretized functions in a wide range of applications, including computational mathematics and machine…

Numerical Analysis · Mathematics 2022-09-30 Andrei Chertkov , Gleb Ryzhakov , Georgii Novikov , Ivan Oseledets

Extending corresponding results for matrix product states [Verstraete and Cirac, PRB 73, 094423 (2006); Schuch et al. PRL 100, 030504 (2008)], it is shown how the approximation error of tree tensor network states (TTNS) can be bounded using…

Quantum Physics · Physics 2026-01-30 Thomas Barthel

Approaching the long-time dynamics of non-Markovian open quantum systems presents a challenging task if the bath is strongly coupled. Recent proposals address this problem through a representation of the so-called process tensor in terms of…

Quantum Physics · Physics 2024-05-20 Valentin Link , Hong-Hao Tu , Walter T. Strunz

This book serves as an introductory yet thorough guide to tensor networks and their applications in quantum computation and quantum information, designed for advanced undergraduate and graduate-level readers. In Part I, foundational topics…

Quantum Physics · Physics 2025-03-07 Mario Collura , Guglielmo Lami , Nishan Ranabhat , Alessandro Santini

Tensor-network Born machines (TNBMs) are quantum-inspired generative models for learning data distributions. Using tensor-network contraction and optimization techniques, the model learns an efficient representation of the target…

Machine Learning · Computer Science 2025-05-07 Matan Ben-Dov , Jing Chen

We devise a deterministic algorithm to efficiently sample high-quality solutions of certain spin-glass systems that encode hard optimization problems. We employ tensor networks to represent the Gibbs distribution of all possible…

Statistical Mechanics · Physics 2021-09-07 Marek M. Rams , Masoud Mohseni , Daniel Eppens , Konrad Jałowiecki , Bartłomiej Gardas

We present a compendium of numerical simulation techniques, based on tensor network methods, aiming to address problems of many-body quantum mechanics on a classical computer. The core setting of this anthology are lattice problems in low…

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…

Numerical Analysis · Mathematics 2025-08-28 Julia Wei , Alec Dektor , Chungen Shen , Zaiwen Wen , Chao Yang

Tree tensor networks (TTNs) provide a compact and structured representation of high-dimensional data, making them valuable in various areas of computational mathematics and physics. In this paper, we present a rigorous mathematical…

Numerical Analysis · Mathematics 2026-04-28 Junyuan He , Zhonghao Sun , Jizu Huang

We investigate the computational power of the recently introduced class of isometric tensor network states (isoTNSs), which generalizes the isometric conditions of the canonical form of one-dimensional matrix-product states to tensor…

Strongly Correlated Electrons · Physics 2022-12-14 Sheng-Hsuan Lin , Michael Zaletel , Frank Pollmann

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…

Statistical Mechanics · Physics 2026-04-29 Gunhee Park , Tomislav Begušić , Si-Jing Du , Johnnie Gray , Garnet Kin-Lic Chan

Quantum optimal control (QOC) provides a systematic framework for achieving high-fidelity operations in quantum systems and plays a central role in tasks such as gate synthesis, state transfer, and pulse design. Existing QOC methods broadly…

Quantum Physics · Physics 2026-04-28 Zeki Zeybek , Rick Mukherjee , Peter Schmelcher

We present a new variational tree tensor network state (TTNS) ansatz, the three-legged tree tensor network state (T3NS). Physical tensors are interspersed with branching tensors. Physical tensors have one physical index and at most two…

Strongly Correlated Electrons · Physics 2018-06-26 Klaas Gunst , Frank Verstraete , Sebastian Wouters , Örs Legeza , Dimitri Van Neck

Sparse tensor networks are commonly used to represent contractions over sparse tensors. Tensor contractions are higher-order analogs of matrix multiplication. Tensor networks arise commonly in many domains of scientific computing and data…

Programming Languages · Computer Science 2024-01-11 Saurabh Raje , Yufan Xu , Atanas Rountev , Edward F. Valeev , Saday Sadayappan

TeNeS (Tensor Network Solver) is a free/libre open-source software program package for calculating two-dimensional many-body quantum states based on the tensor network method and the corner transfer matrix renormalization group (CTMRG)…

Strongly Correlated Electrons · Physics 2022-06-17 Yuichi Motoyama , Tsuyoshi Okubo , Kazuyoshi Yoshimi , Satoshi Morita , Takeo Kato , Naoki Kawashima

We propose a tensor-network (TN) approach for solving classical optimization problems that is inspired by spectral filtering and sampling on quantum states. We first shift and scale an Ising Hamiltonian of the cost function so that all…

Quantum Physics · Physics 2026-02-09 Ryo Watanabe , Joseph Tindall , Shohei Miyakoshi , Hiroshi Ueda

We explain why and numerically confirm that there are no barren plateaus in the energy optimization of isometric tensor network states (TNS) for extensive Hamiltonians with finite-range interactions which are, for example, typical in…

Quantum Physics · Physics 2025-02-17 Qiang Miao , Thomas Barthel

Tensor network (TN), a young mathematical tool of high vitality and great potential, has been undergoing extremely rapid developments in the last two decades, gaining tremendous success in condensed matter physics, atomic physics, quantum…

Computational Physics · Physics 2020-01-31 Shi-Ju Ran , Emanuele Tirrito , Cheng Peng , Xi Chen , Luca Tagliacozzo , Gang Su , Maciej Lewenstein