Planar-perfect-tensor code

Planar-perfect-tensor code[1,2]

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

Quantum codes

Primary Hierarchy

Quantum Domain

Quantum code

Approximate operator-algebra QECC

Operator-algebra QECC (OAQECC)

Quantum error-correcting code (QECC)

Block quantum code

Tensor-network code

Parents

Tensor-network code

Planar-perfect-tensor code

Children

Perfect-tensor code

Planar-perfect tensors are automatically perfect tensors.

\([[5,1,2]]\) rotated surface code

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.

\([[7,1,3]]\) Steane code

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/properties/block/tensor_network/single_tensor/block_perfect.yml.