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PreprintCC BY-NC-ND 4.0HAL

A first introduction to Matrix Product State algorithms for the integration of Lindblad equation

  • Christophe Chatelain
Open at sourcePDFDOICite

Abstract

In this introductory review, we present and compare four algorithms for the numerical integration of the Lindblad equation for one-dimensional quantum lattice systems. All four methods are based on Matrix Product State representations and can be viewed as extensions of the Time-Evolving Block Decimation (TEBD) algorithm to open quantum systems. Two approaches directly integrate the vectorized Lindblad equation, one of them explicitly enforcing the positivity of the density matrix. The other two rely on stochastic unravelings of the Lindblad equation, namely the quantum trajectory and quantum state diffusion approaches. We discuss the principles, numerical implementation, accuracy, and computational efficiency of the different methods, and benchmark them against an exactly solvable free fermion model.

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Cite

BibTeXRIS
BibTeX
@misc{chatelain2026first,
  title = {{A first introduction to Matrix Product State algorithms for the integration of Lindblad equation}},
  author = {Christophe Chatelain},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18841},
  eprint = {2609.18841},
  archivePrefix = {arXiv},
  url = {https://hal.univ-lorraine.fr/hal-05751181v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - A first introduction to Matrix Product State algorithms for the integration of Lindblad equation
AU  - Christophe Chatelain
PY  - 2026
DA  - 2026/09/15
PB  - HAL
DO  - 10.48550/arxiv.2609.18841
UR  - https://hal.univ-lorraine.fr/hal-05751181v1
AB  - In this introductory review, we present and compare four algorithms for the numerical integration of the Lindblad equation for one-dimensional quantum lattice systems. All four methods are based on Matrix Product State representations and can be viewed as extensions of the Time-Evolving Block Decimation (TEBD) algorithm to open quantum systems. Two approaches directly integrate the vectorized Lindblad equation, one of them explicitly enforcing the positivity of the density matrix. The other two rely on stochastic unravelings of the Lindblad equation, namely the quantum trajectory and quantum state diffusion approaches. We discuss the principles, numerical implementation, accuracy, and computational efficiency of the different methods, and benchmark them against an exactly solvable free fermion model.
ER  -