The four-dimensional Chamon code
- URL: http://arxiv.org/abs/2608.20775v1
- Date: Fri, 21 Aug 2026 06:38:24 GMT
- Title: The four-dimensional Chamon code
- Abstract summary: We show that the 4D Chamon code supports three types of restricted-mobility excitations analogous to those of the 3D Chamon code.<n>We also uncover two structural properties relevant to decoding: a hyperplane symmetry and a projection-induced 2D toric-code structure.
- Score: 9.415386554454305
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Fracton models have attracted considerable interest as candidates for quantum memories because of their unconventional ground-state degeneracy (GSD) and restricted-mobility excitations. The four-dimensional (4D) Chamon code introduced in our previous work is constructed via the 4D XYZ product of two two-dimensional (2D) toric codes. Its GSD grows exponentially with the system size, similar to that of the three-dimensional (3D) Chamon code, suggesting that it may be regarded as a 4D generalization of the 3D Chamon code. However, the excitation properties of the 4D Chamon code have not been studied in depth, and a high-performance decoding strategy is still lacking. In this work, we first establish the correspondence between the algebraic structure of the 4D Chamon code and the 4D lattice, thereby characterizing the geometric distributions of qubits and stabilizers. Second, we show that the 4D Chamon code supports three types of restricted-mobility excitations analogous to those of the 3D Chamon code, further supporting its interpretation as a 4D generalization of the 3D Chamon code. Finally, we uncover two structural properties relevant to decoding: a hyperplane symmetry and a projection-induced 2D toric-code structure. By exploiting these properties, we develop a two-layer decoding strategy that decomposes the original decoding problem into multiple independent and parallelizable subproblems. Numerical simulations show that the proposed decoder substantially outperforms BP-OSD in decoding accuracy, demonstrating the benefit of incorporating the intrinsic geometric and algebraic structures of the code into decoder design.
Related papers
- Learning 3D Representations for Spatial Intelligence from Unposed Multi-View Images [81.94999489820974]
UniSplat is a feed-forward framework for learning 3D representations from unposed multi-view images.<n>We introduce a dual-masking strategy that strengthens geometry induction in the encoder.<n>Second, we develop a coarse-to-fine Gaussian splatting strategy that reduces appearance-semantics inconsistencies.<n>Third, we introduce a pose-conditioned recalibration mechanism that interrelates predicted 3D point and semantic maps into the image plane.
arXiv Detail & Related papers (2026-04-12T10:36:18Z) - Reg3D: Reconstructive Geometry Instruction Tuning for 3D Scene Understanding [6.7958985137291235]
Reg3D is a novel Reconstructive Geometry Instruction Tuning framework that incorporates geometry-aware supervision directly into the training process.<n>Our key insight is that effective 3D understanding requires reconstructing underlying geometric structures rather than merely describing them.<n>Experiments on ScanQA, Scan2Cap, ScanRefer, and SQA3D demonstrate that Reg3D delivers substantial performance improvements.
arXiv Detail & Related papers (2025-09-03T18:36:44Z) - High-dimensional quantum XYZ product codes for biased noise [7.749791798931045]
Three-dimensional (3D) quantum XYZ product can construct a class of non-CSS quantum codes by using three classical codes.<n>We study the error-correcting performance of the 3D Chamon code, which is an instance of the 3D XYZ product of three repetition codes.<n>We present the geometric arrangement of the 4D Chamon code within a 4D cubic lattice, demonstrating that it possesses two key characteristics of fracton models.
arXiv Detail & Related papers (2024-08-06T11:54:36Z) - Any2Point: Empowering Any-modality Large Models for Efficient 3D Understanding [83.63231467746598]
We introduce Any2Point, a parameter-efficient method to empower any-modality large models (vision, language, audio) for 3D understanding.
We propose a 3D-to-any (1D or 2D) virtual projection strategy that correlates the input 3D points to the original 1D or 2D positions within the source modality.
arXiv Detail & Related papers (2024-04-11T17:59:45Z) - GOEmbed: Gradient Origin Embeddings for Representation Agnostic 3D Feature Learning [67.61509647032862]
We propose GOEmbed (Gradient Origin Embeddings) that encodes input 2D images into any 3D representation.
Unlike typical prior approaches in which input images are encoded using 2D features extracted from large pre-trained models, or customized features are designed to handle different 3D representations.
arXiv Detail & Related papers (2023-12-14T08:39:39Z) - Layer Codes [0.0]
In three dimensions an analogous simple yet optimal code was not previously known.
The output codes have the special structure of being topological defect networks formed by layers of surface code joined along one-dimensional junctions.
arXiv Detail & Related papers (2023-09-28T15:11:37Z) - NDC-Scene: Boost Monocular 3D Semantic Scene Completion in Normalized
Device Coordinates Space [77.6067460464962]
Monocular 3D Semantic Scene Completion (SSC) has garnered significant attention in recent years due to its potential to predict complex semantics and geometry shapes from a single image, requiring no 3D inputs.
We identify several critical issues in current state-of-the-art methods, including the Feature Ambiguity of projected 2D features in the ray to the 3D space, the Pose Ambiguity of the 3D convolution, and the Imbalance in the 3D convolution across different depth levels.
We devise a novel Normalized Device Coordinates scene completion network (NDC-Scene) that directly extends the 2
arXiv Detail & Related papers (2023-09-26T02:09:52Z) - Unaligned 2D to 3D Translation with Conditional Vector-Quantized Code
Diffusion using Transformers [26.500355873271634]
We propose a simple and novel 2D to 3D synthesis approach based on conditional diffusion with vector-quantized codes.
operating in an information-rich code space enables high-resolution 3D synthesis via full-coverage attention across the views.
arXiv Detail & Related papers (2023-08-27T16:22:09Z) - Engineering 3D Floquet codes by rewinding [0.0]
Floquet codes are quantum error-correcting codes with dynamically generated logical qubits.
We utilize the interpretation of measurements in terms of condensation of topological excitations.
We show that rewinding is advantageous for obtaining a desired set of instantaneous stabilizer groups.
arXiv Detail & Related papers (2023-07-25T17:27:40Z) - PointMCD: Boosting Deep Point Cloud Encoders via Multi-view Cross-modal
Distillation for 3D Shape Recognition [55.38462937452363]
We propose a unified multi-view cross-modal distillation architecture, including a pretrained deep image encoder as the teacher and a deep point encoder as the student.
By pair-wise aligning multi-view visual and geometric descriptors, we can obtain more powerful deep point encoders without exhausting and complicated network modification.
arXiv Detail & Related papers (2022-07-07T07:23:20Z) - Cylindrical and Asymmetrical 3D Convolution Networks for LiDAR
Segmentation [81.02742110604161]
State-of-the-art methods for large-scale driving-scene LiDAR segmentation often project the point clouds to 2D space and then process them via 2D convolution.
We propose a new framework for the outdoor LiDAR segmentation, where cylindrical partition and asymmetrical 3D convolution networks are designed to explore the 3D geometric pat-tern.
Our method achieves the 1st place in the leaderboard of Semantic KITTI and outperforms existing methods on nuScenes with a noticeable margin, about 4%.
arXiv Detail & Related papers (2020-11-19T18:53:11Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.