Kerr-gate injection from linear optics and measurements

Construct a protocol that injects nonlinear Kerr gates using only linear-optical operations and measurements on appropriately chosen non-Gaussian resource states, or more generally shifts all non-Gaussian operations required for universal bosonic computation into offline resource-state preparation.

Background

BEQC uses energy-preserving linear-optical and Kerr gates as universal primitives and provides a Solovay–Kitaev compilation theorem for them. For experimentally realistic architectures, the paper asks whether the nonlinear component can be supplied indirectly through prepared resource states rather than implemented as an online Kerr interaction.

References

This leads to a concrete open question: can nonlinear gates such as the Kerr gate be injected using only linear-optical operations and measurements on appropriately chosen resource states? More generally, can the non-Gaussian operations required for universality be shifted entirely into offline resource-state preparation?

— A physical and universal model of bosonic computations with Solovay-Kitaev theorem  (2609.40226 - Rudolph et al., 30 Sep 2026) in Section 1. Results, subsection “Open questions,” item “Fault tolerance and experimental prospects”