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Title:
Matrix Product Representation of Locality Preserving Unitaries
Speaker:
Abstract:
I'll show recent results about characterization and classification of matrix product unitary operators (MPUOs). After reviewing why one may be interested in MPUOs, we'll start with minimal basics of matrix product states. Then we'll build up the results that end up with fixed-point equations that characterize MPUOs and we'll discuss the implications. Furthermore, we'll go beyond characterization and define an index called 'Rank-Ratio index' that classifies MPUOs. We'll see that it's related to the index that classifies one dimensional quantum cellular automata, introduced by Gross, Nesme, Vogt, Werner. We'll finish the talk with future directions.
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