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Approximate Contraction of Arbitrary Tensor Networks with a Flexible and Efficient Density Matrix Algorithm [PDF]

Quantum
Tensor network contractions are widely used in statistical physics, quantum computing, and computer science. We introduce a method to efficiently approximate tensor network contractions using low-rank approximations, where each intermediate tensor ...
Linjian Ma, Matthew Fishman, Edwin Miles Stoudenmire, Edgar Solomonik   +3 more
doaj   +3 more sources

High-Performance Tensor Contraction without BLAS. [PDF]

SIAM Journal on Scientific Computing, 2016
24 pages, 8 figures, uses ...
Devin A. Matthews
openalex   +4 more sources

Swift: High-Performance Sparse Tensor Contraction for Scientific Applications [PDF]

arXiv.org
In scientific fields such as quantum computing, physics, chemistry, and machine learning, high dimensional data are typically represented using sparse tensors.
Andrew Ensinger, Gabriel Kulp, Victor Agostinelli, Dennis Lyakhov, Lizhong Chen   +4 more
openalex   +2 more sources

The Arithmetic Complexity of Tensor Contraction

Theory of Computing Systems, 2016
We investigate the algebraic complexity of tensor calulus. We consider a generalization of iterated matrix product to tensors and show that the resulting formulas exactly capture VP, the class of polynomial families efficiently computable by arithmetic circuits.
Florent Capelli, Arnaud Durand, S. Mengel   +2 more
semanticscholar   +7 more sources

Optimizing Tensor Network Contraction Using Reinforcement Learning [PDF]

International Conference on Machine Learning, 2022
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.
E. Meirom, Haggai Maron, Shie Mannor, Gal Chechik   +3 more
semanticscholar   +3 more sources

Positive Bias Makes Tensor-Network Contraction Tractable

Proceedings of the 57th Annual ACM Symposium on Theory of Computing
Tensor network contraction is a powerful computational tool in quantum many-body physics, quantum information and quantum chemistry. The complexity of contracting a tensor network is thought to mainly depend on its entanglement properties, as reflected ...
Jiaqing Jiang, Jielun Chen, Norbert Schuch, Dominik Hangleiter   +3 more
semanticscholar   +3 more sources

Validating quantum-supremacy experiments with exact and fast tensor network contraction [PDF]

arXiv.org, 2022
Yong Liu, Yaojian Chen, Chu Guo, Jiawei Song, Xinmin Shi, Lin Gan, Wenzhao Wu, Wei Wu, Haohuan Fu, Xin Liu, Dexun Chen, Guangwen Yang, Jiangang Gao, Gao, Jiangang   +13 more
openalex   +2 more sources

Stack Operation of Tensor Networks

Frontiers in Physics, 2022
The tensor network, as a factorization of tensors, aims at performing the operations that are common for normal tensors, such as addition, contraction, and stacking.
Tianning Zhang, Tianqi Chen, Erping Li, Bo Yang, L. K. Ang   +4 more
doaj   +1 more source

Optimization Methods for Generalized Tensor Contraction

Bulletin of the South Ural State University. Series "Computational Mathematics and Software Engineering", 2020

semanticscholar   +3 more sources

Tensor Network Contractions for #SAT [PDF]

Journal of Statistical Physics, 2015
The computational cost of counting the number of solutions satisfying a Boolean formula, which is a problem instance of #SAT, has proven subtle to quantify. Even when finding individual satisfying solutions is computationally easy (e.g. 2-SAT, which is in P), determining the number of solutions is #P-hard.
Jacob D. Biamonte, Jason Morton, Jacob Turner   +2 more
openaire   +2 more sources