Distributed optimization of Lindblad equations for large-scale cavity QED systems
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911484474294272 |
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| author | Miao, Hui-hui |
| author_facet | Miao, Hui-hui |
| contents | 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 $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04187 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Distributed optimization of Lindblad equations for large-scale cavity QED systems Miao, Hui-hui Quantum Physics 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 $N$. |
| title | Distributed optimization of Lindblad equations for large-scale cavity QED systems |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.04187 |