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Quantum Physics
Title: Fracton models from product codes
(Submitted on 13 Dec 2023 (v1), last revised 9 Apr 2024 (this version, v2))
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 an irregular graph can be obtained as a hypergraph product code. Interestingly, constrained mobility in this model arises only from glassiness 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.
Submission history
From: Brenden Roberts [view email][v1] Wed, 13 Dec 2023 19:03:19 GMT (27489kb,D)
[v2] Tue, 9 Apr 2024 15:32:14 GMT (27481kb,D)
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