Quantum algorithm for the simulation of non-Markovian quantum dynamics using Feynman–Vernon influence functional

In this work, we developed a quantum algorithm for the simulation of non-Markovian quantum dynamics based on the Feynman-Vernon's path integral formulation. The algorithm performs the full path sum and proves to be polynomial either in time or in space, compared to the same classical algorithm, which is exponential in time. In addition, the algorithm has no classical overhead and is equally applicable regardless of whether the temporal entanglement due to non-Markovianity is low or high, making it a unified framework for simulating non-Markovian dynamics in open quantum systems.