Matrix product states and the quantum max-flow/min-cut conjectures
Research output: Contribution to journal › Journal article › Research › peer-review
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.
Original language | English |
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Article number | 102205 |
Journal | Journal of Mathematical Physics |
Volume | 59 |
Issue number | 10 |
Pages (from-to) | 1-11 |
ISSN | 0022-2488 |
DOIs | |
Publication status | Published - 1 Oct 2018 |
Links
- https://arxiv.org/pdf/1801.09106.pdf
Final published version
ID: 226075050