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Seven qubits protecting a qutrit: does a ((7,3,3)) code exist?
Find a three-dimensional subspace of seven qubits that corrects any single-qubit error, or prove that no ((7,3,3)) code exists.
| 1 | { |
| 2 | "domain": "physics-astronomy", |
| 3 | "topics": [ |
| 4 | "quantum-information", |
| 5 | "coding-theory" |
| 6 | ], |
| 7 | "type": "construction", |
| 8 | "also": [ |
| 9 | "proof" |
| 10 | ], |
| 11 | "cover": { |
| 12 | "motif": "spheres" |
| 13 | }, |
| 14 | "source": { |
| 15 | "key": "qiqcop", |
| 16 | "name": "QIQCOP Zoo", |
| 17 | "url": "https://qiqc-op.com/problem/op_4765bc6f2ac91d46/", |
| 18 | "id": "op_4765bc6f2ac91d46", |
| 19 | "curator": "Bikun Li, Qicheng Tang, Changhao Li, Chengkai Zhu, Minbo Gao, Zhong-Xia Shang, Bin Cheng and Naixu Guo", |
| 20 | "poser": "Isaac Chuang, Andrew Cross, Graeme Smith, John Smolin and Bei Zeng", |
| 21 | "status": "unsolved", |
| 22 | "as_of": "2026-10-20", |
| 23 | "catalog": "0521c19bbd38" |
| 24 | } |
| 25 | } |