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The dynamics of open quantum systems can be simulated by unraveling it intoan ensemble of pure state trajectories undergoing non-unitary monitoredevolution, which has recently been shown to undergo measurement-inducedentanglement phase transition. Here, we show that, for an arbitrary decoherencechannel, one can optimize the unraveling scheme to lower the threshold forentanglement phase transition, thereby enabling efficient classical simulationof the open dynamics for a broader range of decoherence rates. Taking noisyrandom unitary circuits as a paradigmatic example, we analytically derive theoptimum unraveling basis that on average minimizes the threshold. Moreover, wepresent a heuristic algorithm that adaptively optimizes the unraveling basisfor given noise channels, also significantly extending the simulatable regime.When applied to noisy Hamiltonian dynamics, the heuristic approach indeedextends the regime of efficient classical simulation based on matrix productstates beyond conventional quantum trajectory methods. Finally, we assess thepossibility of using a quasi-local unraveling, which involves multiple qubitsand time steps, to efficiently simulate open systems with an arbitrarily smallbut finite decoherence rate.

Optimized trajectory unraveling for classical simulation of noisy quantum dynamics