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

• URL: http://arxiv.org/abs/2603.04187v1
• Date: Wed, 04 Mar 2026 15:38:40 GMT
• Title: Distributed optimization of Lindblad equations for large-scale cavity QED systems
• Authors: Hui-hui Miao,
• Abstract summary: This paper proposes a distributed computing framework for solving the Lindblad master equation in large-dimensional cavity QED systems.<n>For unitary terms, a combination of Taylor series approximation and the Cannon algorithm enables distributed matrix exponentiation.<n>Results show that this framework significantly accelerates non-unitary evolution.
• Score: 0.65268245109828
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $O(MN^3)$ 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 $n_{\text{at}}=10$, 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 $N$.

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