Relaxing the derivative-access and slow-variation assumptions

Determine whether the derivative-oracle and slow-analytic assumptions used for simulating time-dependent Hamiltonians can be relaxed while preserving the same or better gate efficiency, including whether standard HAM-T access alone can replace derivative oracles, whether the required periodic extension can be constructed directly from coherent evaluations of the Hamiltonian, and whether the slow condition can be replaced by a more flexible measure of temporal variation.

Background

The paper’s nearly additive query complexity with polylogarithmic precision-dependent gate overhead relies on a slow analytic Hamiltonian representation and, in the general case, coherent access to the derivative together with high-order endpoint derivatives. The discussion identifies relaxing these assumptions as an immediate open direction.

The authors specifically mention replacing derivative access by standard HAM-T access, constructing the periodic extension from coherent evaluations of the Hamiltonian, and replacing the rescaled-time condition by a measure based on temporal variation. These questions concern whether the algorithm’s gate-efficiency advantages can survive under more standard or flexible input models.