stab_15_7_3
[[15,7,3]] skip done[[15, 7, 3]] quantum Hamming code
Description
Self-dual quantum Hamming code that admits permutation-based CZ logical gates. The code is constructed using the CSS construction from the [15,11,3] Hamming code and its [15,4,8] dual simplex code. In the qubit order given by the no…
Introduced in: arxiv:quant-ph/9512032, arxiv:quant-ph/9605021, manual:{J. Harrington and B. W. Reichardt, "Addressable multi-qubit logic via permutations, " Talk at Southwest Quantum Information and Technology (SQuInT) (2011)
Rationale
Audit override: [[15,7,3]] is the r=4 instance of the quantum Hamming family [[2^r-1, 2^r-1-2r, 3]] that QEC/Stabilizer/Codes/Small/QuantumHamming.lean defines parametrically for r ≥ 3. Previous rationale: Audit override: [[15,7,3]] is the r=4 instance of the quantum Hamming family [[2^r-1, 2^r-1-2r, 3]] that QEC/Stabilizer/Codes/Small/QuantumHamming.lean defines parametrically for r ≥ 3. Previous rationale: Audit override: [[15,7,3]] is the r=4 instance of the quantum Hamming family [[2^r-1, 2^r-1-2r, 3]] that QEC/Stabilizer/Codes/Small/QuantumHamming.lean defines parametrically for r ≥ 3. Previous rationale: Audit override: [[15,7,3]] is the r=4 instance of the quantum Hamming family [[2^r-1, 2^r-1-2r, 3]] that QEC/Stabilizer/Codes/QuantumHamming.lean defines parametrically for r ≥ 3. Previous rationale: Audit override: [[15,7,3]] is the r=4 instance of the quantum Hamming family [[2^r-1, 2^r-1-2r, 3]] that QEC/Stabilizer/Codes/QuantumHamming.lean defines parametrically for r ≥ 3. Previous rationale: [[15,7,3]] quantum Hamming code: high-rate distance-3 CSS code; cousin of the already-formalized [[2^r,2^r-r-2,3]] family. Likely a direct corollary of the existing QuantumHamming construction.