\([[144,12,12]]\) gross code[1]
Also known as \((3,3)\) BB code.
Description
A BB code which requires less physical and ancilla qubits (for syndrome extraction) than the surface code with the same number of logical qubits and distance. The gross code is equivalent to 8 copies of the surface code via a constant-depth Clifford circuit, and is an element of a larger family of 2D stabilizer codes [2]. The name stems from the fact that a gross is a dozen dozen.
A different BB QLDPC code with the same parameters was introduced in [3].
Protection
Admits a pseudo-threshold of \(\approx 0.7\%\) for the circuit-based noise model.
Rate
An ancilla-added rate of \(1/24\). In contrast, the distance-13 surface code has ancilla-added rate \(1/338\).
Gates
Clifford gates [4].
Decoding
The GDG sliding-window decoder [5], with a realization achieving a worst-case decoding latency of 3ms per window.AC decoder is faster than ordinary BP-OSD with no reduction of fidelity [6].
Parents
- Bivariate bicycle (BB) code
- 2D lattice stabilizer code — The gross code is equivalent to 8 copies of the surface code via a constant-depth Clifford circuit, and is an element of a larger family of 2D stabilizer codes [2].
Cousin
- Kitaev surface code — The gross code requires less physical and ancilla qubits (for syndrome extraction) than the surface code with the same number of logical qubits and distance. The gross code is equivalent to 8 copies of the surface code via a constant-depth Clifford circuit, and is an element of a larger family of 2D stabilizer codes [2]. An architecture combining the surface and gross codes was proposed in [7].
References
- [1]
- S. Bravyi et al., “High-threshold and low-overhead fault-tolerant quantum memory”, Nature 627, 778 (2024) arXiv:2308.07915 DOI
- [2]
- Z. Liang et al., “Operator algebra and algorithmic construction of boundaries and defects in (2+1)D topological Pauli stabilizer codes”, (2024) arXiv:2410.11942
- [3]
- M. H. Shaw and B. M. Terhal, “Lowering Connectivity Requirements For Bivariate Bicycle Codes Using Morphing Circuits”, (2024) arXiv:2407.16336
- [4]
- A. Cross et al., “Improved QLDPC Surgery: Logical Measurements and Bridging Codes”, (2024) arXiv:2407.18393
- [5]
- A. Gong, S. Cammerer, and J. M. Renes, “Toward Low-latency Iterative Decoding of QLDPC Codes Under Circuit-Level Noise”, (2024) arXiv:2403.18901
- [6]
- S. Wolanski and B. Barber, “Ambiguity Clustering: an accurate and efficient decoder for qLDPC codes”, (2024) arXiv:2406.14527
- [7]
- S. Stein et al., “Architectures for Heterogeneous Quantum Error Correction Codes”, (2024) arXiv:2411.03202
Page edit log
- Victor V. Albert (2024-03-28) — most recent
Cite as:
“\([[144,12,12]]\) gross code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/gross