Variational Quantum Simulation of Dynamical Quantum Phase Transition in Markovian Open Quantum Systems

We investigate dynamical quantum phase transitions (DQPTs) in Markovian open quantum systems using a variational quantum simulation (VQS) algorithm based on quantum state diffusion (QSD). This approach reformulates the Lindblad master equation as an ensemble of pure-state trajectories, enabling efficient simulation of dissipative quantum dynamics with effectively reduced quantum resources. Focusing on the one-dimensional transverse-field Ising model (TFIM), we simulate quench dynamics under both local and global Lindblad dissipation. The QSD-VQS algorithm accurately captures the nonanalytic cusps in the Loschmidt rate function, and reveals their modulation by dissipation strength and system size. Notably, DQPTs are gradually suppressed under strong local dissipation, while they persist under strong global dissipation due to collective environmental effects. Benchmarking against exact Lindblad solutions confirms the high accuracy and scalability of our method.