Search NASA⌕ Search
Home/Archive/DOE OSTI

DOE OSTI · 2999798

Fracton models from product codes

Tan, Yi [Harvard University, Cambridge, MA (United States)] (ORCID:0009000941926137)·Roberts, Brenden [Harvard University, Cambridge, MA (United States)] (ORCID:0000000231071878)·Tantivasadakarn, Nathanan [California Institute of Technology, Pasadena, CA (United States)] (ORCID:0000000152952124)·Yoshida, Beni [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada)]·Yao, Norman Y. [Harvard University, Cambridge, MA (United States)] (ORCID:0000000301947266)
View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

FractonsQuantum error correctionQuantum memoriesTopological phases of matter

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Tan, Yi [Harvard University, Cambridge, MA (United States)] (ORCID:0009000941926137), Roberts, Brenden [Harvard University, Cambridge, MA (United States)] (ORCID:0000000231071878), Tantivasadakarn, Nathanan [California Institute of Technology, Pasadena, CA (United States)] (ORCID:0000000152952124), Yoshida, Beni [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada)], Yao, Norman Y. [Harvard University, Cambridge, MA (United States)] (ORCID:0000000301947266). 2025-09-22. Fracton models from product codes. https://doi.org/10.1103/f48m-rlh3

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related reports

DOE OSTI2025

Braiding for the win: Harnessing braiding statistics in topological states to play quantum games

Nonlocal quantum games provide proof of principle that quantum resources can confer an advantage at certain tasks. They also provide a compelling way to explore the computational utility of phases of matter on quantum hardware. In a recent paper [O. Hart et al., Phys. Rev. Lett. 134, 130602 (2025)], we demonstrated that a toric code resource state conferred advantage at a certain nonlocal game, which remained robust to small deformations of the resource state. In this paper we demonstrate that this robust advantage is a generic property of resource states drawn from topological or fracton ordered phases of quantum matter. To this end, we illustrate how several other states from paradigmatic topological and fracton ordered phases can function as resources for suitably defined nonlocal games, notably the three-dimensional toric-code phase, the X-cube fracton phase, and the double-semion phase. The key in every case is to design a nonlocal game that harnesses the characteristic braiding processes of a quantum phase as a source of contextuality. We unify the strategies that take advantage of mutual statistics by relating the operators to be measured to order and disorder parameters of an underlying generalized symmetry-breaking phase transition. Additionally, by connecting the win probability to twist products, we show that success at the game serves as a many-body entanglement witness. Namely, if the players implement a perfect quantum strategy on large length scales, the quantum state they share cannot be connected to a trivial product state via a constant-depth local unitary circuit. Lastly, we massively generalize the family of games that admit perfect strategies when codewords of homological quantum error-correcting codes are used as resources.

Fractons↗