Efficient gate decomposition of the Howe-based cloner implementation

Develop an efficient elementary-gate decomposition of the Howe transforms and Clebsch–Gordan coupling used in the Stinespring implementation of the structured-state cloners.

Background

The paper gives an exact representation-theoretic circuit architecture for the Stinespring dilation of its cloners, using Howe transforms and a Clebsch–Gordan coupling. This specifies the isometry mathematically but does not establish an efficient implementation in a standard gate model.

The authors explicitly leave the efficient decomposition of these components into elementary gates unresolved.

References

The circuit specifies the isometry exactly; an efficient decomposition of the Howe transforms and the coupling into elementary gates is left open.

— Approximate cloning of structured pure states  (2610.06723 - Herasymenko et al., 5 Oct 2026) in Section 5, subsection “Stinespring dilation and complementary channels”