Spectral conditions for improved quantum algorithms

Identify spectral constraints on the memory kernel \(K\) that enable improved quantum algorithms for linear Volterra integro-differential equations, including systems in which the memory term stabilizes an otherwise unstable Markovian dynamics.

Background

The paper notes that certain memory kernels can stabilize dynamics whose Markovian component is unstable, but its general-kernel algorithm is established primarily in the dissipative short-term-memory regime. It remains unresolved whether spectral information about the kernel can be used to design efficient algorithms in these stabilizing or otherwise difficult regimes.

References

Are there constraints we can place on the spectrum of $K$ that can help us find better algorithms? For instance, some forms of $K$ can stabilize a dynamics that would be otherwise unstable. Would it be possible to develop efficient algorithms for such systems?

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