Chaos is often viewed as an obstacle to control. However, the field of controlling chaos shows that chaotic classical systems can actually be steered efficiently using very small perturbations, by harnessing their instability and ergodic behaviour . In direct analogy, recent work has demonstrated that localized quantum states can be transported along trajectories related to the classical dynamics of the system, enabling fast and precise quantum state control. This approach has been successfully applied both to single-particle quantum systems [1,2] and to interacting bosonic systems described by the Bose–Hubbard model [3]. While interesting, this approach is classical at its core and does not take advantage of quantum interference. However, quantum chaos in general offers universal features, namely the exponential decay of the Loschmidt echo as well as the statistical properties described by random matrix theory, that replace the classical notions of instability and ergodicity in the context of quantum systems (even in the absence of a classical limit). We argue that these features are essential for full state controllability and allow the translation of classical chaos control to the quantum realm [4].
[1] S. Tomsovic, J. D. Urbina, and Klaus Richter, Controlling Quantum Chaos: Optimal Coherent Targeting, PRL 130.2 (2023): 020201
[2] S. Tomsovic, J. D. Urbina, and Klaus Richter, Controlling quantum chaos: Time-dependent kicked rotor, PRE 108 (2023): 044202
[3] L. Beringer, M. Steinhuber, J. D. Urbina, K. Richter, S. Tomsovic, Controlling many-body quantum chaos: Bose-Hubbard systems, New J. Phys (2024): 26 073002
[4] L. Beringer, M. Steinhuber, K. Richter, S. Tomsovic, Quantum Chaos as an Essential Resource for Full Quantum State Controllability, arxiv:2512.13385