Transforming Lindblad Equations into Systems of Real-Valued Linear Equations: Performance Optimization and
Iosif Meyerov1, Evgeny Kozinov1, Alexey Liniov1
1Mathematical Center, Lobachevsky University, 603950 Nizhni Novgorod, Russia.
Entropy (Basel, Switzerland)
|December 8, 2020
Summary
This study presents a parallel computing approach to efficiently simulate complex quantum systems using Lindblad master equations. The new method overcomes memory limitations, enabling larger and more detailed quantum system modeling.
Area of Science:
- Quantum physics
- Computational physics
- Quantum information science
Background:
- Modern supercomputers enable advanced numerical studies of open many-body quantum systems.
- Markovian quantum master equations, particularly the Lindblad form, are crucial for modeling quantum system evolution.
- Previous implementations faced significant memory constraints for large-scale models.
Purpose of the Study:
- To develop a scalable and memory-efficient algorithm for solving Lindblad master equations.
- To enable the simulation of larger open quantum systems than previously feasible.
- To address the computational bottlenecks in quantum system modeling.
Main Methods:
- Transformation of Lindblad equations into a system of ordinary differential equations using generalized Gell-Mann matrices.
- Development and implementation of a parallel cluster-based algorithm.
- Analysis of computational complexity for dense and sparse Lindbladians.
Main Results:
- A parallel cluster-based implementation overcoming previous memory limitations was developed.
- The algorithm successfully integrated a sparse Lindbladian model of dimension N=2000.
- A dense random Lindbladian model of dimension N=200 was integrated using 25 compute nodes.
Conclusions:
- The parallel implementation significantly enhances the feasibility of large-scale quantum system simulations.
- This approach opens new avenues for numerical studies in quantum optics, cavity quantum electrodynamics, and optomechanics.
- The method provides a powerful tool for investigating complex open quantum systems with unprecedented detail.
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