Matrix product states and the quantum max-flow/min-cut conjectures
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© 2018 Author(s). In this note, we discuss the geometry of matrix product states with periodic boundary conditions and provide three infinite sequences of examples where the quantum max-flow is strictly less than the quantum min-cut. In the first, we fix the underlying graph to be a 4-cycle and verify a prediction of Hastings that inequality occurs for infinitely many bond dimensions. In the second, we generalize this result to a 2d-cycle. In the third, we show that the 2d-cycle with periodic boundary conditions gives inequality for all d when all bond dimensions equal two, namely, a gap of at least 2d−2 between the quantum max-flow and the quantum min-cut.
author list (cited authors)
Gesmundo, F., Landsberg, J. M., & Walter, M.
complete list of authors
Gesmundo, Fulvio||Landsberg, JM||Walter, Michael