Generalizing projective-representation linearisations to non-abelian groups

Construct a linearisation of projective representations of finite non-abelian groups that generalizes the abelian linearisation construction and supports efficient Anyonic Symmetry Learning beyond finite abelian groups.

Background

For finite abelian groups, the paper linearises projective representations using self-orthogonal linear error-correcting codes, thereby reducing Projective Anyonic Symmetry Learning to linear-representation instances. The authors explain that the construction relies on the fact that power maps are homomorphisms in abelian groups, a property that generally fails for non-abelian groups, and explicitly identify extending the construction as an unresolved question.

References

A natural question is whether this linearisation construction can be generalised to projective representations of finite non-abelian groups.

— Learning quantum symmetries  (2609.38085 - Holt et al., 29 Sep 2026) in Section 'Outlook and future directions', paragraph 'Linearising projective representations and coding theory'

We leave it as an open question whether other properties of the code, e.g. the minimum distance, have any relevance to the induced distribution.

— Learning quantum symmetries  (2609.38085 - Holt et al., 29 Sep 2026) in Section 'Optimising sample rate and number of copies needed per sample', subsection 'Optimising without zero-row-sum condition'