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Combinatorial optimization has wide applications from industry to natural science. Ising machines bring an emerging computing paradigm for efficiently solving a combinatorial optimization problem by searching a ground state of a given Ising…

Statistical Mechanics · Physics 2024-07-16 Kentaro Ohno , Tatsuhiko Shirai , Nozomu Togawa

Here we explore which heuristic quantum algorithms for combinatorial optimization might be most practical to try out on a small fault-tolerant quantum computer. We compile circuits for several variants of quantum accelerated simulated…

Variational tensor network optimization has become a powerful tool for studying classical statistical models in two dimensions. However, its application to three-dimensional systems remains limited, primarily due to the high computational…

Statistical Mechanics · Physics 2025-10-14 Xia-Ze Xu , Tong-Yu Lin , Guang-Ming Zhang

For combinatorial optimization problems that can be formulated as Ising or Potts spin systems, the Mean Field (MF) approximation yields a versatile and simple ANN heuristic, Deterministic Annealing. For assignment problems the situation is…

Disordered Systems and Neural Networks · Physics 2007-05-23 Bo Soderberg , Henrik Jonsson

We combine the fields of heuristic optimization and optimal stopping. We propose a strategy for benchmarking randomized optimization algorithms that minimizes the expected total cost for obtaining a good solution with an optimal number of…

Quantum Physics · Physics 2016-12-07 Walter Vinci , Daniel A. Lidar

Tensor network states (TNS) are a promising but numerically challenging tool for simulating two-dimensional (2D) quantum many-body problems. We introduce an isometric restriction of the TNS ansatz that allows for highly efficient…

Strongly Correlated Electrons · Physics 2020-02-10 Michael P. Zaletel , Frank Pollmann

Tensor networks (TNs) are one of the best available tools to study many-body quantum systems. TNs are particularly suitable for one-dimensional local Hamiltonians, while their performance for generic geometries is mainly limited by two…

Quantum Physics · Physics 2026-04-08 Apimuk Sornsaeng , Itai Arad , Dario Poletti

Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…

Optimization and Control · Mathematics 2016-02-29 Farbod Roosta-Khorasani , Michael W. Mahoney

Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…

Machine Learning · Computer Science 2022-04-26 Martin J. A. Schuetz , J. Kyle Brubaker , Helmut G. Katzgraber

Traditional Monte Carlo integration using uniform random sampling exhibits degraded efficiency in low-regularity or high-dimensional problems. We propose a novel deep learning framework based on deterministic number-theoretic sampling…

Numerical Analysis · Mathematics 2025-07-03 Yu Yang , Pingan He , Xiaoling Peng , Qiaolin He

Quantum computing has the potential for disruptive change in many sectors of industry, especially in materials science and optimization. In this paper, we describe how the Turbine Balancing Problem can be solved with quantum computing,…

We study tensor networks as a model of arithmetic computation for evaluating multilinear maps. These capture any algorithm based on low border rank tensor decompositions, such as $O(n^{\omega+\epsilon})$ time matrix multiplication, and in…

Computational Complexity · Computer Science 2018-11-16 Per Austrin , Petteri Kaski , Kaie Kubjas

We develop coarse-graining tensor renormalization group algorithms to compute physical properties of two-dimensional lattice models on finite periodic lattices. Two different coarse-graining strategies, one based on the tensor…

Strongly Correlated Electrons · Physics 2016-07-12 Hui-Hai Zhao , Zhi-Yuan Xie , Tao Xiang , Masatoshi Imada

Neural network quantum states (NQS) have emerged as a powerful and flexible framework for addressing quantum many-body problems. While successful for model Hamiltonians, their application to molecular systems remains challenging for several…

Chemical Physics · Physics 2025-07-28 Zibo Wu , Bohan Zhang , Wei-Hai Fang , Zhendong Li

Combinatorial optimization is a broadly attractive area for potential quantum advantage, but no quantum algorithm has yet made the leap. Noise in quantum hardware remains a challenge, and more sophisticated quantum-classical algorithms are…

The Steiner tree problem is a well-known problem in network design, routing, and VLSI design. Given a graph, edge costs, and a set of dedicated vertices (terminals), the Steiner tree problem asks to output a sub-graph that connects all…

Artificial Intelligence · Computer Science 2020-11-10 Johannes K. Fichte , Markus Hecher , Andre Schidler

Finding the ground states of the Ising Hamiltonian [1] maps to various combinatorial optimization problems in biology, medicine, wireless communications, artificial intelligence, and social network. So far no efficient classical and quantum…

Quantum Physics · Physics 2014-10-30 Alireza Marandi , Zhe Wang , Kenta Takata , Robert L. Byer , Yoshihisa Yamamoto

A promising approach to achieve computational supremacy over the classical von Neumann architecture explores classical and quantum hardware as Ising machines. The minimisation of the Ising Hamiltonian is known to be NP-hard problem for…

Quantum Physics · Physics 2020-08-04 Kirill P. Kalinin , Natalia G. Berloff

Entanglement forging based variational algorithms leverage the bi-partition of quantum systems for addressing ground state problems. The primary limitation of these approaches lies in the exponential summation required over the numerous…

Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-$N$ tensor from exponential…

Strongly Correlated Electrons · Physics 2022-05-31 Hao Chen , Thomas Barthel