Preparation and verification of tensor network states

Categorical Tensor Network States

Jacob D. Biamonte, Stephen R. Clark and Dieter Jaksch Oxford University Computing Laboratory, Parks Road Oxford, OX1 3QD, United Kingdom Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore Keble College, Parks Road, University of Oxford, Oxford OX1 3PG, United Kingdom Clarendon Laboratory, Department of Physics, University of Oxford,...

Lectures on Tensor Network States

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Tensor Network States: Algorithms and Applications

Neural network representation of tensor network and chiral states

We study the representational power of a Boltzmann machine (a type of neural network) in quantum many-body systems. We prove that any (local) tensor network state has a (local) neural network representation. The construction is almost optimal in the sense that the number of parameters in the neural network representation is almost linear in the number of nonzero parameters in the tensor network...

Second renormalization of tensor-network states.

We propose a second renormalization group method to handle the tensor-network states or models. This method dramatically reduces the truncation error of the tensor renormalization group. It allows physical quantities of classical tensor-network models or tensor-network ground states of quantum systems to be accurately and efficiently determined.