Optimality of isotypic-compression resources

Determine whether the circuit depths and number of ancillae used by the isotypic-compression circuit for stabilizer-state learning are optimal, or whether they can be reduced further.

Background

The algorithm achieves near-optimal sample complexity but relies on an isotypic-compression circuit whose implementation dominates the computational complexity. The paper leaves unresolved whether the stated depth and ancilla requirements are necessary or can be improved.

References

An open question is whether one can obtain a proper agnostic learner for \mathsf{RM}(n,2), as well as for stabilizer states.

— Marton's conjecture in polynomial time  (2609.20771 - Arunachalam et al., 17 Sep 2026) in Section 1, subsection “Quadratic Goldreich-Levin,” footnote following the corollary on quadratic decomposition

It is also open whether our circuit depths and the number of ancillae employed in the isotypic compression circuit are optimal, or can be further reduced.

— Sample-optimal learning of stabilizer states  (2609.10974 - Chang et al., 10 Sep 2026) in Section 3, Discussion