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  • Tutorial
  • Open Access

Taming Quantum Systems: A Tutorial for Using Shortcuts-To-Adiabaticity, Quantum Optimal Control, and Reinforcement Learning

Callum W. Duncan1,2, Pablo M. Poggi2,3,*, Marin Bukov4, Nikolaj Thomas Zinner5,6, and Steve Campbell7,8,9

  • *Contact author: pablo.poggi@strath.ac.uk
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PRX Quantum 6, 040201 – Published 31 October, 2025

DOI: https://doi.org/10.1103/j8c7-v2hd

Abstract

Precise manipulation of quantum effects at the atomic and nanoscale has become an essential task in ongoing scientific and technological endeavors. Quantum control methods are thus routinely exploited for research in areas such as quantum materials, quantum chemistry, and atomic and molecular physics, as well as in the development of quantum technologies like computing, simulation, and sensing. Here, we present a pedagogical introduction to the basics of quantum control methods in tutorial form, with the aim of providing newcomers to the field with the core concepts and practical tools to use these methods in their research. We focus on three areas: shortcuts to adiabaticity, quantum optimal control, and machine-learning-based control. We lay out the basic theoretical elements of each area in a pedagogical way and describe their application to a series of example cases. For these, we include detailed analytical derivations as well as extensive numerical results. As an outlook, we discuss quantum control methods in the broader context of quantum technologies development and complex quantum systems research, outlining potential connections and synergies between them.

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Popular Summary

Quantum control techniques have revolutionized the manipulation of complex systems, enabling precise control over their constituents. Achieving this level of control is essential for a wide range of applications such as quantum-enhanced sensing, quantum chemistry, and developing quantum technologies. In this tutorial, we provide a pedagogical introduction to state-of-the-art approaches to controlling quantum systems with a focus on shortcuts-to-adiabaticity, quantum optimal control, and reinforcement learning. The key theoretical aspects of each technique is elucidated through the use of accessible examples, and which clearly demonstrate their respective strengths and limitations.

While control is often seen as a means to an end, we argue that identifying what are the necessary resources and requirements to achieve command over complex systems offers an insightful window into advancing our understanding of the dynamics of quantum systems. Furthermore, by carefully introducing each approach, we establish that hybridized protocols present a viable route to overcoming current control bottlenecks, e.g., in relation to their scalability and experimental implementation.

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PRX Quantum 6, 040201– Published 31 October, 2025
  • Received 13 May 2025
  • Revised 7 August 2025
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