Direct incorporation of logical error rate into SAT-based code design

Incorporate the logical error rate directly into the SAT-based quantum code design problem, rather than treating it as an emergent property evaluated after code construction.

Background

The SAT formulation developed in the paper enforces stabilizer commutation and error-detection or error-correction constraints, while the logical error rate is evaluated afterward through numerical memory experiments. The authors note that logical error rate depends on the full code and is difficult to express directly within the SAT formulation. They therefore identify direct incorporation of this performance metric into code design as an unresolved problem.

References

It is unlikely that one can easily incorporate the logical error rate into the SAT formulation or any formulation for code design since this is a property of the full code that must be measured by a separate (numerical) experiment. We leave as an open problem the possibility to directly incorporate logical error rate into the code design problem in future work.

— Satisfying Quantum Codes: Physics-Informed and Hardware-Aware Code Design with SAT Solvers  (2608.23460 - DalFavero et al., 24 Aug 2026) in Section 6, Conclusion