Incorporating list decoding into DQI

Determine whether list-decoding algorithms for algebraic geometry codes, and more generally list-decoding methods beyond the unique-decoding regime, can be incorporated effectively into Decoded Quantum Interferometry to permit larger decoding radii and improve optimization guarantees.

Background

The DQI construction developed in the paper relies on coherent unique syndrome decoding in the dual code, with the decoding radius limited by the unique-decoding radius. Although efficient list-decoding algorithms for algebraic geometry codes are known, using them would require modifying the quantum decoding step to handle multiple candidate error vectors.

The conclusion leaves unresolved whether such list-decoding procedures can be integrated into DQI and whether doing so would enable operation at larger decoding radii, potentially strengthening the resulting satisfaction guarantees.

References

Another interesting direction would be to understand how list-decoding algorithms for algebraic geometry codes can be incorporated into the DQI framework and, more generally, whether DQI can effectively exploit list-decoding methods beyond the unique-decoding regime. Such an extension could potentially allow DQI to operate with larger decoding radii and thereby improve the resulting optimization guarantees.

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