Continuous-time dynamics of noisy quantum circuits with arbitrary neural-network ansätze

We present a numerical method to simulate the dynamics of low-entropy open quantum systems. The method is based on compressing the Hilbert space to a time-dependent ``corner" subspace that supports faithful representations of the density matrix. We show that this compression enables one to efficiently simulate systems with moderate entropy irrespective of the quantum state's degree of entanglement. In addition, we propose a second compression step, which consists in representing each state of the corner subspace with a neural-network ansatz. This enables the use of a wider class of ansätze for the dynamics of open quantum systems and for noisy quantum circuit simulation. We present benchmarks of the method using different ansätze. We then apply the method to (i) dissipative spin models and (ii) to noisy quantum circuits.