Tile Codes: High-Efficiency Quantum Codes on a Lattice with Boundary
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909578172563456 |
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| author | Steffan, Vincent Choe, Shin Ho Breuckmann, Nikolas P. Pereira, Francisco Revson Fernandes Eberhardt, Jens Niklas |
| author_facet | Steffan, Vincent Choe, Shin Ho Breuckmann, Nikolas P. Pereira, Francisco Revson Fernandes Eberhardt, Jens Niklas |
| contents | We introduce tile codes, a simple yet powerful way of constructing quantum codes that are local on a planar 2D-lattice. Tile codes generalize the usual surface code by allowing for a bit more flexibility in terms of locality and stabilizer weight. Our construction does not compromise on the fact that the codes are local on a lattice with open boundary conditions. Despite its simplicity, we use our construction to find codes with parameters $[[288, 8, 12]]$ using weight-6 stabilizers and $[[288, 8, 14]]$ using weight-8 stabilizers, outperforming all previously known constructions in this direction. Allowing for a slightly higher non-locality, we find a $[[512, 18, 19]]$ code using weight-8 stabilizers, which outperforms the rotated surface code by a factor of more than 12. Our approach provides a unified framework for understanding the structure of codes that are local on a 2D planar lattice and offers a systematic way to explore the space of possible code parameters. In particular, due to its simplicity, the construction naturally accommodates various types of boundary conditions and stabilizer configurations, making it a versatile tool for quantum error correction code design. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_09171 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tile Codes: High-Efficiency Quantum Codes on a Lattice with Boundary Steffan, Vincent Choe, Shin Ho Breuckmann, Nikolas P. Pereira, Francisco Revson Fernandes Eberhardt, Jens Niklas Quantum Physics We introduce tile codes, a simple yet powerful way of constructing quantum codes that are local on a planar 2D-lattice. Tile codes generalize the usual surface code by allowing for a bit more flexibility in terms of locality and stabilizer weight. Our construction does not compromise on the fact that the codes are local on a lattice with open boundary conditions. Despite its simplicity, we use our construction to find codes with parameters $[[288, 8, 12]]$ using weight-6 stabilizers and $[[288, 8, 14]]$ using weight-8 stabilizers, outperforming all previously known constructions in this direction. Allowing for a slightly higher non-locality, we find a $[[512, 18, 19]]$ code using weight-8 stabilizers, which outperforms the rotated surface code by a factor of more than 12. Our approach provides a unified framework for understanding the structure of codes that are local on a 2D planar lattice and offers a systematic way to explore the space of possible code parameters. In particular, due to its simplicity, the construction naturally accommodates various types of boundary conditions and stabilizer configurations, making it a versatile tool for quantum error correction code design. |
| title | Tile Codes: High-Efficiency Quantum Codes on a Lattice with Boundary |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2504.09171 |