Solving Quantum Master Equations with Deep Quantum Neural Networks

TL;DR

This paper introduces a deep quantum neural network approach to solve quantum master equations, enabling efficient modeling of open quantum systems and demonstrating its effectiveness on spin models.

Contribution

The paper presents a novel variational method using deep quantum neural networks to solve quantum master equations, highlighting advantages like avoiding barren plateaus and resource efficiency.

Findings

Successfully modeled dynamics of quantum spin systems

Achieved accurate stationary state predictions

Demonstrated method's scalability and efficiency

Abstract

Deep quantum neural networks may provide a promising way to achieve quantum learning advantage with noisy intermediate scale quantum devices. Here, we use deep quantum feedforward 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 the absence of barren plateaus, efficient quantum analogue of the backpropagation 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.