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Given a quantum state we can construct its MPS (Matrix Product State) representation by doing a series of singular value decompositions. Given the freedom to choose arbitrary bond dimensions the MPS representation is powerful enough to represent any quantum state.

I have read that PEPS (Projected Entangled-Pair State) is seen as a natural extension of MPS to general graphs. Then given a quantum state and some graph is there an algorithm that constructs a PEPS equal to that state on that graph ? Any reference to such an algorithm would be much appreciated.

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  • $\begingroup$ It would be helpful, both to people answering your question and people subsequently trying to learn from it, if you define what your acronyms mean $\endgroup$
    – By Symmetry
    Commented Oct 1, 2018 at 11:06

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You can always embed an MPS into the 2D graph -- possibly by using edges twice -- and then use the same method as for MPS. Alternatively, you can e.g. block the graph into slices such as to obtain a 1D structure and then first to the MPS decomposition and subsequently decompose the slices.

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