Fracton models from product codes
-
1.
Harvard University
-
2.
California Institute of Technology
-
3.
Perimeter Institute
Abstract
We explore a deep connection between fracton order and product codes. In particular, we propose and analyze conditions on classical seed codes which lead to fracton order in the resulting quantum product codes. Depending on the properties of the input codes, product codes can realize either Type-I or Type-II fracton models, in both nonlocal and local constructions. For the nonlocal case, we show that a recently proposed model of lineons on nonlocal graphs can be obtained as a hypergraph product code. Interestingly, constrained mobility in this model arises only from energy barriers associated with the graph. For the local case, we introduce a novel type of classical LDPC code defined on a planar aperiodic tiling. By considering the specific example of the pinwheel tiling, we demonstrate the systematic construction of local Type-I and Type-II fracton models as product codes. Our work establishes product codes as a natural setting for exploring fracton order.
Copyright and License
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Acknowledgement
We gratefully acknowledge the insight of and discussions with H.-Y. Hu, Z.-X. Luo, S.-H. Shao, T. Schuster, and C. Zhang. We are particularly indebted to H. Kamal for discussions leading to the origination of this project. This work was supported in part by the Department of Energy, Office of Science, Office of High Energy Physics under QuantISED Award No. DE-SC0019380 (Geoflow consortium) and by the NSF STAQ program. B.R. acknowledges support from the Harvard Quantum Initiative Postdoctoral Fellowship in Science Engineering. N.Y.Y. acknowledges support from a Simons Investigator award.
Supplemental Material
Files
f48m-rlh3.pdf
Files
(1.3 MB)
| Name | Size | Download all |
|---|---|---|
|
md5:0bca11f43bc0b64bbb6ead184ba8658b
|
882.7 kB | Preview Download |
|
md5:91fbe4b2bde7b67b768cfc0d34d597a1
|
432.4 kB | Preview Download |
Additional details
Related works
- Is new version of
- Discussion Paper: arXiv:2312.08462 (arXiv)
- Is supplemented by
- Supplemental Material: https://journals.aps.org/prresearch/supplemental/10.1103/f48m-rlh3/fracton_product_code_PRR_supp.pdf (URL)
Funding
- United States Department of Energy
- DE-SC0019380
- Harvard University
- Harvard Quantum Initiative Postdoctoral Fellowship -
- Simons Foundation
Dates
- Accepted
-
2025-06-10