Solving the Liouvillian Gap with Artificial Neural Networks

Understand

We propose a machine-learning inspired variational method to obtain the Liouvillian gap, which plays a crucial role in characterizing the relaxation time and dissipative phase transitions of open quantum systems.

• By using the "spin bi-base mapping", we map the density matrix to a pure restricted-Boltzmann-machine (RBM) state and transform the Liouvillian superoperator to a rank-two non-Hermitian operator.
• The Liouvillian gap can be obtained by a variational real-time evolution algorithm under this non-Hermitian operator.
• We apply our method to the dissipative Heisenberg model in both one and two dimensions.