Bayesian Optimization for Robust State Preparation in Quantum Many-Body Systems

Tizian Blatz; Joyce Kwan; Julian Léonard; Annabelle Bohrdt

doi:10.22331/q-2024-06-27-1388

Bayesian Optimization for Robust State Preparation in Quantum Many-Body Systems

Tizian Blatz^1,2, Joyce Kwan³, Julian Léonard⁴, and Annabelle Bohrdt^2,5

¹Department of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Munich D-80333, Germany
²Munich Center for Quantum Science and Technology (MCQST), Munich D-80799, Germany
³Department of Physics, Harvard University, Cambridge, MA 02138, USA
⁴Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, Vienna 1020, Austria
⁵Institute of Theoretical Physics, University of Regensburg, Regensburg D-93053, Germany

Published:	2024-06-27, volume 8, page 1388
Eprint:	arXiv:2312.09253v2
Doi:	https://doi.org/10.22331/q-2024-06-27-1388
Citation:	Quantum 8, 1388 (2024).

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Abstract

New generations of ultracold-atom experiments are continually raising the demand for efficient solutions to optimal control problems. Here, we apply Bayesian optimization to improve a state-preparation protocol recently implemented in an ultracold-atom system to realize a two-particle fractional quantum Hall state. Compared to manual ramp design, we demonstrate the superior performance of our optimization approach in a numerical simulation – resulting in a protocol that is 10x faster at the same fidelity, even when taking into account experimentally realistic levels of disorder in the system. We extensively analyze and discuss questions of robustness and the relationship between numerical simulation and experimental realization, and how to make the best use of the surrogate model trained during optimization. We find that numerical simulation can be expected to substantially reduce the number of experiments that need to be performed with even the most basic transfer learning techniques. The proposed protocol and workflow will pave the way toward the realization of more complex many-body quantum states in experiments.

Featured image: Proposed optimization strategy exploiting numerical resources to boost optimization efficiency in an experiment. Depending on the task at hand, several avenues with varying experimental costs may be explored:
The most straightforward way is to directly implement the optimization result obtained from simulation in the experiment, requiring only a single evaluation of the protocol’s quality. On top of this, the BO surrogate model can provide a sensitivity analysis that can be exploited to manually calibrate only the most sensitive protocol parameters in ∼10 experimental evaluations. Finally, when substantial adaptation to the experimental setting is necessary, online optimization can be performed in ∼100 to ∼1000 iterations directly with the experiment. Transfer-learning approaches can leverage numerical resources to accelerate training significantly, e.g., by initializing the surrogate model used for training in the experiment with training data from the simulation.
The prospective reduction of the number of cost-function evaluations in the experiment is crucial in the context of optical lattice systems where typical snapshot-based detection schemes require many experimental runs to determine an accurate figure of merit. In our work, we highlight and motivate these three scenarios by comparing the numerical simulation of an idealized system to a more realistic description of the experimental setting that takes experimental disorder into account.

Popular summary

In our work, we improve state preparation in quantum simulators by using machine learning and computer simulation. The quantum simulation experiments we investigate are setups that offer high levels of control over a few to hundreds of atoms and allow probing the phenomena of quantum mechanics. Today, one of the biggest challenges in these setups is to prepare specific target states with interesting properties. To achieve state preparation in an efficient and robust way, we apply Bayesian optimization to a numerical simulation of an experiment. We find that our method is highly capable of controlling the system and we develop a general strategy to make experiments more efficient through simulation.

The optimized solution can create the target state 10 times faster than what has been done in the experiment. It does so without sacrificing preparation fidelity and we show it to be remarkably robust to the disorder expected in an experimental system. Additionally, we demonstrate that the optimization results obtained in a simulation can directly be used in or transferred to an experiment in a simple and straightforward way.
Therefore, our novel optimization strategy can significantly expand the range of states experiments have access to and can reduce the time in the lab it takes to find them.

► BibTeX data

@article{Blatz2024bayesian,
  doi = {10.22331/q-2024-06-27-1388},
  url = {https://doi.org/10.22331/q-2024-06-27-1388},
  title = {Bayesian {O}ptimization for {R}obust {S}tate {P}reparation in {Q}uantum {M}any-{B}ody {S}ystems},
  author = {Blatz, Tizian and Kwan, Joyce and L{\'{e}}onard, Julian and Bohrdt, Annabelle},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1388},
  month = jun,
  year = {2024}
}

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Cited by

[1] F. A. Palm, J. Kwan, B. Bakkali-Hassani, M. Greiner, U. Schollwöck, N. Goldman, and F. Grusdt, "Growing extended Laughlin states in a quantum gas microscope: A patchwork construction", Physical Review Research 6 1, 013198 (2024).

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