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

TL;DR

This paper introduces a distributed computational framework that significantly accelerates the simulation of large-scale open quantum systems described by Lindblad equations, by exploiting sparsity and advanced algorithms to reduce complexity and memory usage.

Contribution

It develops a novel distributed approach combining the Cannon algorithm and sparsity exploitation to efficiently solve Lindblad equations in large cavity QED systems, reducing computational complexity and memory.

Findings

Reduces non-unitary term complexity from O(MN^3) to O(MN)

Achieves a Hamiltonian dimension reduction to 5.63% of the full size for n_{at}=10

Significantly accelerates the simulation of large open quantum systems

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 $N$.