# Hamiltonian and Liouvillian learning in weakly-dissipative quantum many-body systems

**Authors:** Tobias Olsacher, Tristan Kraft, Christian Kokail, Barbara Kraus, Peter Zoller  
**arXiv:** [2405.06768](https://arxiv.org/abs/2405.06768)  
**Date:** 2024-05-10  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2405.06768v2/

## Key points

- Authors Tobias Olsacher, Tristan Kraft, Christian Kokail, Barbara Kraus, and Peter Zoller focus on weakly dissipative many-body systems in analog quantum simulation.
- They explore Hamiltonian and Liouvillian learning methods to decipher operator content.
- Learning error initially decreases with the inverse square root of experimental runs due to shot noise dominance.
- Eventually, learning error stabilizes at a constant level, aiding in identifying missing ansatz terms.
- (Re-)parametrizing ans\"atze by manipulating parameter dependencies is a key technique for pinpointing relevant system parameters effectively.
- The approach relies on classical post-processing methods, which is advantageous for dealing with limited experimental data availability.
- The researchers apply their techniques to two experimentally relevant spin models to showcase efficacy and robustness in unraveling quantum dynamics within weakly-dissipative many-body systems.

## Summary

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In their paper titled "Hamiltonian and Liouvillian learning in weakly-dissipative quantum many-body systems," authors Tobias Olsacher, Tristan Kraft, Christian Kokail, Barbara Kraus, and Peter Zoller delve into the realm of analog quantum simulation from non-equilibrium quench dynamics. They focus on weakly dissipative many-body systems and explore the intricacies of Hamiltonian and Liouvillian learning. The researchers present a comprehensive analysis of various methods and strategies aimed at deciphering the operator content of the Hamiltonian and the Lindblad operators of the Liouvillian. This parameter is evaluated as a function of the number of experimental runs conducted. The authors observe an initial decrease in the learning error with the inverse square root of the number of runs, attributing this trend to shot noise dominating errors in reconstructed parameters. Interestingly, they note that eventually, the learning error stabilizes at a constant level, enabling them to identify missing ansatz terms within their models. A pivotal component of their approach involves (re-)parametrizing ans\"atze by introducing and manipulating dependencies between parameters. This innovative technique allows them to pinpoint relevant system parameters effectively, thereby streamlining the complexity associated with the learning task. Notably, this (re-)parametrization process relies solely on classical post-processing methods, which proves advantageous given the finite amount of data typically available from experimental setups. To illustrate and validate their methodologies, Olsacher et al. apply their techniques to two experimentally relevant spin models. Through detailed comparisons and analyses, they showcase the efficacy and robustness of their proposed approaches in unraveling intricate quantum dynamics within weakly-dissipative many-body systems. Overall, this research contributes valuable insights towards advancing analog quantum simulation techniques for studying non-equilibrium phenomena in complex quantum systems.