Distributed optimization of Lindblad equations for large-scale cavity QED systems

This paper proposes a distributed computing framework for solving the Lindblad master equation in large-dimensional cavity QED systems. By leveraging the sparsity of the jump operator and combining this approach with the Cannon algorithm, the computational complexity of non-unitary terms is reduced from O\(MN³\) to O(MN). For unitary terms, a combination of Taylor series approximation and the Cannon algorithm enables distributed matrix exponentiation, though scalability is limited by cross-processor communication. The proposed dynamic subspace construction method further reduces the Hamiltonian dimension: when n_at=10, the dimension is reduced to 5.63\% of the full Hamiltonian, with a memory footprint of only 0.32\%. Results show that this framework significantly accelerates non-unitary evolution, providing a feasible solution for simulating large-scale open quantum systems where the number of dissipative channels M is much larger than the Hamiltonian dimension N.