Coset-based quantum LDPC codes expand beyond 2BGA constructions with competitive circuit-level thresholds
The coset generalization of 2BGA codes yields new finite-length quantum LDPC examples with practical thresholds and a compact syndrome schedule. Evidence consists of exhaustive search plus circuit-level Monte Carlo; distance scaling and gate implementations remain open. The approach strengthens the case that algebraic LDPC families may outpace surface-code overhead this decade if fabrication and decoding keep pace.
If the observed thresholds hold under leakage and crosstalk models typical of fixed-frequency transmons, these codes could reduce the spacetime overhead for 10^-12 logical error rates by roughly an order of magnitude compared with rotated surface codes of equivalent distance. Follow-on experiments on 100-qubit devices will be required to confirm whether the depth-w+2 schedule preserves the simulated advantage once control electronics constraints are included.
Barg et al.: A weight-6 coset code will be fabricated and decoded on a 127-qubit superconducting processor with logical error rate below 5e-4 by end of 2027.
Sources (3)
- [1]Primary Source(https://arxiv.org/abs/2606.17268)
- [2]Supporting Source(https://arxiv.org/abs/2308.07915)
- [3]Supporting Source(https://arxiv.org/abs/2406.14445)