Efficient Classical Simulation of Lindblad Dynamics

While many proof of principle experiments have been performed the fundamental computational power of NISQ computers is unclear. One path to approach this problem is to investigate methods on classical computer that can efficently simulate noisy quantum systems. In limits where this is possible a NISQ computer can fundamentally not achive quantum advantage. Many quantum systems described by the Lindblad equation have properties which make them especially amenable to classical solution. Here we outline our approach to the classical simulation of such systems using a non-linear approximation to the Lindblad equation. We will present our results regarding the systems we have been able to exclude as potential demonstrations of quantum advantage, and also discuss potential future applications of the classical method we have developed.