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valbert4 committed Jul 2, 2024
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code_id: holographic_tensor

name: 'Holographic tensor-network code'
introduced: '\cite{arxiv:1503.06237,arxiv:1601.01694,arXiv:1801.05289,arxiv:2009.10329,arxiv:2109.11996}'
introduced: '\cite{arxiv:1503.06237,arxiv:1601.01694,arXiv:1801.05289,arxiv:2009.10329}'

description: |
Quantum Lego code whose encoding isometry forms a holographic tensor network, i.e., a tensor network associated with a tiling of hyperbolic space.
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A family of conjectured perfect-tensor codes is quantum MDS \cite{arxiv:quant-ph/0312164}.'
- code_id: mds
detail: 'MDS codes can be used to obtain perfect-tensor codes with minimal support \cite{arxiv:1306.2536,arxiv:1506.08857,arxiv:1701.03359}.'
- code_id: combinatorial_design
detail: 'Combinatorial designs and \(d\)-uniform quantum states are related \cite{arXiv:1506.08857}.'
- code_id: orthogonal_array
detail: 'Orthogonal arrays and \(d\)-uniform quantum states are related \cite{arXiv:1404.3586,arxiv:1708.05946}.'
- code_id: qudit_cluster_state
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