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\([[72,12,6]]\) BB6 code[1]

Alternative names: \((6,6)\) BB6 code.

Description

A bivariate bicycle (BB) code with parameters \([[72,12,6]]\) and weight-six stabilizer generators [1].

One defining presentation uses \((\ell,m)=(6,6)\) with \(x^{\ell}=y^{m}=1\), and \(A=x^3+y+y^2\), \(B=y^3+x+x^2\) in \(\mathbb{F}_2[x,y]/(x^{\ell}-1,y^{m}-1)\) [1][1; Table 3].

Rate

Ancilla-added encoding rate is \(1/12\), using \(n_a=n=72\) ancilla qubits.

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Primary Hierarchy

Quantum Domain
Qubit Kingdom
Qubit codeQECC Quantum
Union stabilizer (USt) codeQECC Quantum
Qubit stabilizer codeStabilizer Hamiltonian-based Qubit QECC Quantum
Coherent-parity-check (CPC) code
Qubit CSS codeCSS Stabilizer Hamiltonian-based QECC Quantum
Generalized homological-product qubit CSS codeQLDPC Qubit Generalized homological-product CSS Stabilizer Hamiltonian-based QECC Quantum
Bivariate bicycle (BB) codeGeneralized homological-product Lattice stabilizer CSS Stabilizer Hamiltonian-based QECC Quantum
Parents
Bivariate bicycle (BB) code
\([[72,12,6]]\) BB6 code

References

[1]
S. Bravyi, A. W. Cross, J. M. Gambetta, D. Maslov, P. Rall, and T. J. Yoder, “High-threshold and low-overhead fault-tolerant quantum memory”, Nature 627, 778 (2024) arXiv:2308.07915 DOI
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Zoo Code ID: bb72

Cite as:
“\([[72,12,6]]\) BB6 code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/bb72
BibTeX:
@incollection{eczoo_bb72, title={\([[72,12,6]]\) BB6 code}, booktitle={The Error Correction Zoo}, year={2026}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/bb72} }
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Permanent link:
https://errorcorrectionzoo.org/c/bb72

Cite as:

“\([[72,12,6]]\) BB6 code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/bb72

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/qldpc/balanced_product/lp/bb/bb72.yml.