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    Tensor network method for reversible classical computation

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    Date Issued
    2018-03-08
    Publisher Version
    10.1103/PhysRevE.97.033303
    Author(s)
    Yang, Zhi-Cheng
    Kourtis, Stefanos
    Chamon, Claudio
    Mucciolo, Eduardo R.
    Ruckenstein, Andrei E.
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    Permanent Link
    https://hdl.handle.net/2144/35766
    Version
    Accepted manuscript
    Citation (published version)
    Zhi-Cheng Yang, Stefanos Kourtis, Claudio Chamon, Eduardo R Mucciolo, Andrei E Ruckenstein. 2018. "Tensor network method for reversible classical computation." PHYSICAL REVIEW E, Volume 97, Issue 3, pp. ? - ? (13). https://doi.org/10.1103/PhysRevE.97.033303
    Abstract
    We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017)]. By encoding the truth table of each vertex constraint in a tensor, the total number of solutions compatible with partial inputs and outputs at the boundary can be represented as the full contraction of a tensor network. We introduce an iterative compression-decimation (ICD) scheme that performs this contraction efficiently. The ICD algorithm first propagates local constraints to longer ranges via repeated contraction-decomposition sweeps over all lattice bonds, thus achieving compression on a given length scale. It then decimates the lattice via coarse-graining tensor contractions. Repeated iterations of these two steps gradually collapse the tensor network and ultimately yield the exact tensor trace for large systems, without the need for manual control of tensor dimensions. Our protocol allows us to obtain the exact number of solutions for computations where a naive enumeration would take astronomically long times.
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