Solving quantum master equations with deep quantum neural networks

Deep quantum neural networks may provide a promising way to achieve a quantum learning advantage with noisy intermediate-scale quantum devices. Here, we use deep quantum feed-forward neural networks capable of universal quantum computation to represent the mixed states for open quantum many-body systems and introduce a variational method with quantum derivatives to solve the master equation for dynamics and stationary states. Owning to the special structure of the quantum networks, this approach enjoys a number of notable features, including an efficient quantum analog of the back-propagation algorithm, resource-saving reuse of hidden qubits, general applicability independent of dimensionality and entanglement properties, as well as the convenient implementation of symmetries. As proof-of-principle demonstrations, we apply this approach to both one-dimensional transverse field Ising and two-dimensional J(1) -J(2) models with dissipation, and show that it can efficiently capture their dynamics and stationary states with a desired accuracy.

Automated summary

Deep quantum neural networks provide a promising way to achieve a quantum learning advantage with noisy intermediate-scale quantum devices. This approach uses deep quantum feed-forward neural networks to represent the mixed states of open quantum many-body systems, and introduces a variational method with quantum derivatives to solve the dynamics and stationary states. The special structure of the quantum networks allows for efficient quantum analog of back-propagation algorithm, resource-saving reuse of hidden qubits, general applicability, and convenient implementation of symmetries.