Abstract
In condensed matter physics, finding the wave function of a quantum many-body system is the most important issue. Theoretical development in recent years includes a wave function approximation using a tensor network. At first glance, the tensor network looks very similar to neural network diagrams, but how are they actually related? In this chapter we will see the relation and the mapping, and that the restricted Boltzmann machine is closely related to tensor networks.
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Notes
- 1.
The tensor network is not a physical network arranged spatially. It is a graph specifying how spins etc. are intertwined with each other.
- 2.
- 3.
Einstein’s convention is the understanding that indices that appear more than once will be summed over.
- 4.
The relations among the parameters of the networks are discussed in [127].
- 5.
There is also a study that uses product pooling to see a correspondence [128].
- 6.
MERA stands for Multiscale Entanglement Renormalization Ansatz.
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Tanaka, A., Tomiya, A., Hashimoto, K. (2021). Quantum Manybody Systems, Tensor Networks and Neural Networks. In: Deep Learning and Physics. Mathematical Physics Studies. Springer, Singapore. https://doi.org/10.1007/978-981-33-6108-9_11
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DOI: https://doi.org/10.1007/978-981-33-6108-9_11
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