Alternative names: Block-perfect-tensor code, Perfect-tangle code.
Description
Block quantum code whose encoding isometry is a block perfect tensor, i.e., a tensor which remains an isometry under partitions into two contiguous components in a fixed plane. This code stems from a planar maximally entangled state [3].Cousins
- Category-based quantum code— Several modular fusion categories can be used to define planar-perfect tensors [1].
- Surface-code-fragment (SCF) holographic code— The encoding of the heptagon holographic code is a holographic tensor network consisting of the encoding isometry for the \([[5,1,2]]\) rotated surface code, which is a planar-perfect tensor.
- Heptagon holographic code— The encoding of the heptagon holographic code is a holographic tensor network consisting of the encoding isometry for the Steane code, which is a planar-perfect tensor.
Member of code lists
Primary Hierarchy
Parents
Planar-perfect-tensor code
Children
Planar-perfect tensors are automatically perfect tensors.
The \([[5,1,2]]\) rotated surface code is the smallest SCF holographic code. The encoding of more general SCF holographic codes is a holographic tensor network consisting of the encoding isometry for the \([[5,1,2]]\) rotated surface code, which is a planar-perfect tensor.
The Steane code is the smallest heptagon holographic code. The encoding of more general heptagon holographic codes is a holographic tensor network consisting of the encoding isometry for the Steane code, which is a planar-perfect tensor.
References
- [1]
- J. Berger and T. J. Osborne, “Perfect tangles”, (2018) arXiv:1804.03199
- [2]
- R. J. Harris, N. A. McMahon, G. K. Brennen, and T. M. Stace, “Calderbank-Shor-Steane holographic quantum error-correcting codes”, Physical Review A 98, (2018) arXiv:1806.06472 DOI
- [3]
- M. Doroudiani and V. Karimipour, “Planar maximally entangled states”, Physical Review A 102, (2020) arXiv:2004.00906 DOI
Page edit log
- Victor V. Albert (2024-07-01) — most recent
Cite as:
“Planar-perfect-tensor code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/block_perfect