Generalize error detection to superpositions with more than two sectors

Generalize the distribute–collapse error-detection strategy from the two-sector case to non-normal matrix product states with K>2 components in the GHZ-like superposition, for which the required error-detection construction remains unresolved.

Background

The paper applies its distribute–collapse framework to non-normal matrix product states represented as superpositions of K normal matrix product states, but develops the construction explicitly only for K=2. In that case, the ancillary distributed GHZ state is collapsed using an error-detected collapse primitive, heralding successful preparation of the target superposition.

Extending the construction to K>2 is identified as requiring a generalization of the error-detection strategy. Such a generalization would broaden the framework from binary GHZ-like control to multi-sector superpositions while preserving the paper’s low-overhead, constant-depth error-detection objective.

References

We focus on the case $K=2$ as it is most naturally expressed in terms of the framework introduced here; we expect that $K>2$ will require a generalization of our error detection strategy, and we leave it as an avenue for future research.

— Resilience Beyond the Light Cone: Error-Detected Primitives for Practical Dynamic Circuits  (2609.08925 - Smith et al., 8 Sep 2026) in Section 3.2.3, “Non-normal matrix product states”