Applicability of DQI beyond algebraic geometry codes

Investigate whether Decoded Quantum Interferometry can be applied effectively to code families beyond algebraic geometry codes, provided that those families fit within the Decoded Quantum Interferometry framework, and compare its performance across broader code families.

Background

The paper introduces Curve-based Optimal Function Intersection (COFI) to extend Decoded Quantum Interferometry (DQI) from Reed–Solomon and one-point Hermitian codes to broader families of algebraic geometry codes, including Suzuki, extended norm–trace, and two-point Hermitian codes.

The conclusion explicitly identifies the unresolved issue of whether the DQI framework requires algebraic geometry structure or can exploit other efficiently decodable code families. Resolving this would clarify the generality of DQI and could reveal additional code families with improved quantum optimization guarantees.

References

An open direction is to explore DQI performance across broader families of codes. In particular, it may not be necessary to restrict to algebraic geometry codes, provided the chosen family fits within the DQI framework. We therefore aim to extend these comparisons to other code families and investigate whether DQI can be applied beyond the AG setting.

— COFI-DQI: Curve-based Optimal Function Intersection via Decoded Quantum Interferometry  (2609.31484 - Matthews et al., 25 Sep 2026) in Section 5, Conclusion

It remains an open question whether DQI can also achieve quantum advantage for algebraically unstructured problems such as random spin glass models.

— Gibbs Sampling in the Shattered Phase by Decoded Quantum Interferometry  (2609.40345 - Zhou et al., 30 Sep 2026) in Section 1, Introduction