Variational Lindblad with Magnus Expansion

QSD_SME_VQA

Building on the close relationship between unraveled Lindblad dynamics, stochastic Magnus integrators, and variational quantum simulation, we propose a high-order scheme for solving the quantum state diffusion equation using exponential integrators. This formulation facilitates the simulation of wavefunction trajectories within the established framework of variational quantum algorithms for time evolution. Our algorithm significantly enhances robustness in two key aspects: the stability of the simulation with large time steps, and the reduction in the number of quantum trajectories required to accurately simulate the Lindblad dynamics in terms of the ensemble average.

Files:

• classical_test: testing the stochastic Magnus expansion-based schemes (Scheme I-IV) via the exact wavefunction trajectory method
• quantum_test: testing the validity of the ansatz-based variational simulation of quantum dynamics, implemented using Qiskit

Three different models are simulated to examine the performance of the algorithm:

• test_TFIM.py: the transverse field Ising model (TFIM) with damping
• test_FMO.py: the Fenna-Matthews-Olson (FMO) complex dynamics
• test_RPM.py: the radical pair model (RPM) for avian compass dynamics

References:

Jia-Cheng Huang, Hao-En Li, Yi-Cheng Wang, Guang-Ze Zhang, Jun Li, Han-Shi Hu, “Towards robust variational quantum simulation of Lindblad dynamics via stochastic Magnus expansion”, PRX Quantum 6, 040312 (2025), [doi][arXiv:2503.22099]