Optimal trajectory unraveling for classical simulation of noisy quantum dynamics

Simulating noisy many-body quantum dynamics in realistic quantum devices using trajectory unraveling is limited by the growth of quantum entanglement. In generic systems, it is previously shown that entanglement in the steady state of trajectories undergoes a phase transition from a volume- to an area-law scaling when increasing the noise rate, allowing for efficient classical simulation only above the critical noise rate. In this work, we introduce an optimal unraveling basis that minimizes the average entanglement entropy in trajectories, reduces the critical noise rate, and therefore extends the regime for efficient classical simulation. We first demonstrate our method in the numerical simulation of noisy Haar random circuits. We then provide an analytical understanding of the optimal basis by mapping the random circuit to an effective classical spin model. Furthermore, we simulate the trajectories of noisy Hamiltonian dynamics and show that the optimal unraveling basis significantly extended the regime of efficient simulation using matrix product states.