Sierpinski prism model code

Sierpinski prism model code[1,2]

Alternative names: Sierpinsky fractal spin-liquid (SFSL) code, Yoshida first-order fractal spin-liquid code.

Description

A fractal type-I fracton CSS code defined on a cubic lattice [3; Eq. (D22)]. The code admits an excitation-moving operator shaped like a Sierpinski triangle [3; Fig. 2].

Cousins

Newman-Moore code— The Sierpinski prism model code is a hypergraph product of the repetition code and the Newman-Moore code [4], and can be formulated directly as an LP code [5].
Repetition code— The Sierpinski prism model code is a hypergraph product of the repetition code and the Newman-Moore code [4], and can be formulated directly as an LP code [5].
Lifted-product (LP) code— The Sierpinski prism model code is a hypergraph product of the repetition code and the Newman-Moore code [4], and can be formulated directly as an LP code [5].
3D surface code— The Sierpinski prism model code admits a topological defect network construction out of 3D surface codes on triangular prisms [6,7].
Haah cubic code (CC)— The Haah A-code can be written in a similar form as the Sierpinski prism model code [7].

Member of code lists

Primary Hierarchy

Quantum Domain

Qubit Kingdom

Qubit codeQECC Quantum

Union stabilizer (USt) codeQECC Quantum

Qubit stabilizer codeStabilizer Hamiltonian-based Qubit QECC Quantum

Coherent-parity-check (CPC) code

Qubit CSS codeCSS Stabilizer Qubit Hamiltonian-based QECC Quantum

Parents

Qubit CSS code

Fracton stabilizer codeLattice stabilizer QLDPC Stabilizer Hamiltonian-based QECC Quantum

The Sierpinski prism model code is a fractal type-I fracton code [3].

Hypergraph product (HGP) codeGeneralized homological-product Lattice stabilizer QLDPC CSS Stabilizer Qubit Hamiltonian-based QECC Quantum

The Sierpinski prism model code is a hypergraph product of the repetition code and the Newman-Moore code [4], and can be formulated directly as an LP code [5].

Sierpinski prism model code

References

[1]: C. Castelnovo and C. Chamon, “Topological quantum glassiness”, Philosophical Magazine 92, 304 (2012) arXiv:1108.2051 DOI
[2]: B. Yoshida, “Exotic topological order in fractal spin liquids”, Physical Review B 88, (2013) arXiv:1302.6248 DOI
[3]: A. Dua, I. H. Kim, M. Cheng, and D. J. Williamson, “Sorting topological stabilizer models in three dimensions”, Physical Review B 100, (2019) arXiv:1908.08049 DOI
[4]: T. Rakovszky and V. Khemani, “The Physics of (good) LDPC Codes II. Product constructions”, (2024) arXiv:2402.16831
[5]: Y. Tan, B. Roberts, N. Tantivasadakarn, B. Yoshida, and N. Y. Yao, “Fracton models from product codes”, (2024) arXiv:2312.08462
[6]: D. Aasen, D. Bulmash, A. Prem, K. Slagle, and D. J. Williamson, “Topological defect networks for fractons of all types”, Physical Review Research 2, (2020) arXiv:2002.05166 DOI
[7]: Z. Song, A. Dua, W. Shirley, and D. J. Williamson, “Topological Defect Network Representations of Fracton Stabilizer Codes”, PRX Quantum 4, (2023) arXiv:2112.14717 DOI

Page edit log

Nathanan Tantivasadakarn (2024-06-27) — most recent
Victor V. Albert (2023-04-12)

Cite as:

“Sierpinski prism model code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/sierpinsky_fractal_liquid

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/fracton/fractal_spin_liquid/sierpinsky_fractal_liquid.yml.