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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.05479 |
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| _version_ | 1866908784501194752 |
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| author | Roberts, Brenden Koh, Jin Ming Tan, Yi Yao, Norman Y. |
| author_facet | Roberts, Brenden Koh, Jin Ming Tan, Yi Yao, Norman Y. |
| contents | The existence of self-correcting quantum memories in three dimensions is a long-standing open question at the interface between quantum computing and many-body physics. We take the perspective that large contributions to the entropy arising from fine-tuned spatial symmetries, including the assumption of an underlying regular lattice, are responsible for fundamental challenges to realizing self-correction. Accordingly, we introduce a class of disordered quantum codes, which we call "cored product codes". These codes are derived from classical factors via the hypergraph product but undergo a coring procedure which allows them to be embedded in a lower number of spatial dimensions while preserving code properties. As a specific example, we focus on a fractal code based on the aperiodic pinwheel tiling as the classical factor and perform finite temperature numerical simulations on the resulting three-dimensional quantum memory. We provide evidence that, below a critical temperature, the memory lifetime increases with system size for codes up to 60000 qubits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05479 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cored product codes for quantum self-correction in three dimensions Roberts, Brenden Koh, Jin Ming Tan, Yi Yao, Norman Y. Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics The existence of self-correcting quantum memories in three dimensions is a long-standing open question at the interface between quantum computing and many-body physics. We take the perspective that large contributions to the entropy arising from fine-tuned spatial symmetries, including the assumption of an underlying regular lattice, are responsible for fundamental challenges to realizing self-correction. Accordingly, we introduce a class of disordered quantum codes, which we call "cored product codes". These codes are derived from classical factors via the hypergraph product but undergo a coring procedure which allows them to be embedded in a lower number of spatial dimensions while preserving code properties. As a specific example, we focus on a fractal code based on the aperiodic pinwheel tiling as the classical factor and perform finite temperature numerical simulations on the resulting three-dimensional quantum memory. We provide evidence that, below a critical temperature, the memory lifetime increases with system size for codes up to 60000 qubits. |
| title | Cored product codes for quantum self-correction in three dimensions |
| topic | Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2510.05479 |