Algebraic structures enabling geometrically efficient fast-forwarding

Characterize which algebraic structures permit fast-forwarding of Hamiltonian dynamics while retaining an efficient geometrically local circuit implementation.

Background

The construction achieves near-optimal depth for a broad class of time-independent, finite-range Hamiltonians but does not determine when Hamiltonian dynamics can be fast-forwarded. The paper highlights a further unresolved issue: identifying algebraic structures that enable fast-forwarding without sacrificing efficient implementation under geometric locality constraints. This question concerns the interaction between algebraic simplifications of the dynamics and the spatial costs of distributing coherent controls.