Results 21 to 30 of about 737,908 (337)
On the Optimal Linear Contraction Order of Tree Tensor Networks, and Beyond [PDF]
SIAM Journal on Scientific Computing, 2022 The contraction cost of a tensor network depends on the contraction order. However, the optimal contraction ordering problem is known to be NP-hard. We show that the linear contraction ordering problem for tree tensor networks admits a polynomial-time ...
Mihail Stoian +2 more
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Approximate Contraction of Arbitrary Tensor Networks with a Flexible and Efficient Density Matrix Algorithm [PDF]
QuantumTensor 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 +3 more
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Effective Utilization of Tensor Symmetry in Operation Optimization of Tensor Contraction Expressions
Procedia Computer Science, 2012 AbstractThe optimization of tensor expressions with hundreds of terms is required for the development of accurate quantum chemistry models such as the coupled cluster method. In this paper, we address the effective exploitation of symmetry properties of tensors in performing algebraic transformations for minimizing operation count of tensor expressions.
Pai-Wei Lai +5 more
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High-Performance Tensor Contraction without Transposition [PDF]
SIAM Journal on Scientific Computing, 2016 Tensor computations---in particular tensor contraction (TC)---are important kernels in many scientific computing applications. Due to the fundamental similarity of TC to matrix multiplication and to the availability of optimized implementations such as ...
D. Matthews
semanticscholar +5 more sources
Using Ensemble Learning to Improve Automatic Vectorization of Tensor Contraction Program
IEEE Access, 2018 Automatic vectorization is crucial for improving the performance of computationally intensive programs. Existing compilers use conservative optimization strategies for automatic vectorization, which, in many cases, lead to the loss of vectorization ...
Hui Liu, Rongcai Zhao, Kai Nie
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On the Decomposition of Tensors by Contraction [PDF]
Proceedings of the National Academy of Sciences, 1952 F. D. Murnaghan
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Treelike process tensor contraction for automated compression of environments [PDF]
Physical Review ResearchThe algorithm “automated compression of environments” (ACE) [M. Cygorek et al., Nat. Phys. 18, 662 (2022)1745-247310.1038/s41567-022-01544-9] provides a versatile way of simulating an extremely broad class of open quantum systems.
Moritz Cygorek +3 more
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Lecture Notes of Tensor Network Contractions [PDF]
, 2019 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 information ...
Chen, Xi +6 more
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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 +2 more
semanticscholar +7 more sources
Positive Bias Makes Tensor-Network Contraction Tractable [PDF]
Symposium on the Theory of ComputingTensor 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 +3 more
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