Improved complexity for Markovianization beyond exponential-sum restrictions

Determine whether the restrictions imposed on the memory kernel by the Markovianization approach can be relaxed while retaining improved quantum-simulation complexity for linear Volterra integro-differential equations.

Background

The Markovianization method converts structured-kernel VIDEs into larger systems of ordinary differential equations, enabling the use of quantum ODE solvers. In the paper, this method requires the memory kernel to admit an approximation by a sum of real exponentials. The authors leave unresolved whether comparable complexity improvements survive under weaker structural assumptions.

References

To improve the complexity of this class of algorithms beyond linear multistep methods might require additional constraints on the dynamics. For our Markovianization approach, we highly restricted the kernels. Is it possible to remove some constraints and still end up with improved complexity?

— Quantum simulation of non-Markovian dynamical systems  (2608.13533 - Ameri et al., 13 Aug 2026) in Section 1, subsection “Outlook,” paragraph “Higher-order methods”