Solving quantum master equations with deep quantum neural networks

• Published in: Physical review research Vol. 4; no. 1; p. 013097
• Main Authors: Liu, Zidu, Duan, L.-M., Deng, Dong-Ling
• Format: Journal Article
• Language: English
• Published: American Physical Society 01-02-2022
• ISSN: 2643-1564; 2643-1564
• DOI: 10.1103/PhysRevResearch.4.013097

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.