Algorithmic quantum simulation of memory effects
  We propose a method for the algorithmic quantum simulation of memory effects described by integrodifferential evolution equations. It consists in the systematic use of perturbation theory techniques and a Markovian quantum simulator. Our method aims to efficiently simulate both completely positive and nonpositive dynamics without the requirement of engineering non-Markovian environments. Finally, we find that small error bounds can be reached with polynomially scaling resources, evaluated as the time required for the simulation. 
U. Alvarez-Rodriguez, R. Di Candia, J. Casanova, M. Sanz, E. Solano
quant-ph cond-mat.mes-hall