Block encoding for nonlinear polymerization kinetics

Develop a block-encoding formulation applicable to nonlinear polymerization kinetics involving multiple time-evolving chemical species, including batch polymerization with time-dependent monomer concentrations and macromer incorporation reactions.

Background

The paper’s constructions assume a linear kinetic equation. Linearity is obtained by treating monomer concentrations as constant and restricting reactions among polymer species to first order. Under batch conditions or in macromer incorporation reactions, multiple chemical species evolve simultaneously, producing nonlinear kinetics that are not covered by the present formulation.

The unresolved task is to extend the block-encoding framework beyond these linear assumptions while retaining an efficient quantum representation of the resulting polymerization dynamics. The authors explicitly identify this as an important open problem.