Existing quantum algorithms for dynamical system simulation—from Hamiltonian simulation to linear and nonlinear differential equations—primarily address Markovian dynamics, where future evolution depends only on the current state. In this work, we turn our attention to non-Markovian systems, in which future evolution depends on the system’s full history. Specifically, we develop efficient quantum algorithms for dissipative linear Volterra integro-differential equations (VIDEs) with convolution memory kernels. For general kernels, our approach is efficient under a natural short-term memory condition. We further establish lower bounds showing that, in the absence of this condition, simulating general VIDEs becomes intractable on quantum computers. As an application, we discuss the linear coarse-graining framework. *We strongly encourage attendees to use their full name (and if possible, their UMD credentials) to join the zoom session.*