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Lecture 2

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Tensor networks has been introduced in quantum information<br />

theory.<br />

Example<br />

1. TT (tensor trains, Oseledets & Tyrtyshnikov ) and HT<br />

(Hackbusch & Kühn) formats are tensor networks.<br />

2. the canonical format is not (directly) a tensor network.<br />

x 1<br />

k 1<br />

tensor networks<br />

ki<br />

x 1<br />

closed tensor<br />

network<br />

tensor networks<br />

u 2 [x k i k j ]<br />

2

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