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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)
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Summary
This summary is machine-generated.

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.

Keywords:
Lindblad equationMPIopen quantum systemsparallel computingperformance optimization

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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.