Forked Physics-Informed Neural Networks for Non-Markovian Open Quantum Dynamics and Control

Research Question and Approach

Traditional methods for quantum system simulation and control are typically decoupled, relying on separate numerical integrators and optimization algorithms. While Physics-Informed Neural Networks (PINNs) have emerged as a way to unify these tasks, they struggle with non-Markovian environments, where memory effects require solving coupled auxiliary operator equations. This paper introduces the Forked Physics-Informed Neural Network (FPINN) to address these optimization conflicts. The authors propose an architecture that uses a shared trunk for common temporal features and dedicated branches for the auxiliary operator, the density matrix, and control fields. By applying selective gradient flow, the FPINN decouples the optimization objectives at the gradient level, allowing the network to perform joint simulation and control without the instability common in monolithic PINN designs.

The researchers validated the FPINN framework using a two-qubit Heisenberg XXX model. In simulation tasks, the FPINN accurately reproduced non-Markovian dynamics, including decoherence and information backflow, matching reference solutions obtained via Runge-Kutta 4th-order (RK4) methods. For quantum control—specifically state preparation—the FPINN demonstrated superior fidelity compared to established methods like GRAPE and CRAB, particularly in regimes with strong dissipation and Markovian characteristics. Furthermore, the FPINN generated smoother control pulses, which are more practical for experimental implementation. The end-to-end differentiable nature of the framework allows it to handle time-dependent Hamiltonians seamlessly without requiring architectural modifications.

This work provides a unified, efficient paradigm for the simulation and control of open quantum systems. By successfully integrating non-Markovian memory effects into a neural network framework, the FPINN offers a robust tool for quantum information science. Its ability to generate high-fidelity, smooth control pulses while simultaneously simulating complex environmental interactions makes it a promising candidate for applications in quantum computing and quantum simulation, where environmental noise is a persistent challenge.