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Control of quantum systems is at the core of quantum technologies, such as quantum computation based on quantum logical gates and quantum sensing. Such applications of quantum control require reaching a given target state (or propagator) with high fidelity via fast, ideally optimal, processes [1]. Physical implementations also impose robustness with respect to noise of the experimental parameters or to their imperfect knowledge. We develop a geometrical procedure, referred to as robust inverse optimization (RIO) [2-4], which allows a time- or energy- optimal pulse controls that are immune to errors. The procedure is demonstrated on IBM’s quantum computers via a digital version of RIO [5].

We also design optimal and robust stimulated Raman exact passage (STIREP), taking into account the presence of a lossy intermediate state [6].

Optimal control and RIO techniques find applications in the manipulation of Bose-Einstein condensates [1], including nonlinear effects [7], and in optimal quantum sensing [8]. Furthermore, they are shown to provide an energy shortcut of quantum protocols, which outperform Shortcut-To-Adiabaticity (STA) processes [9].

[1] Q. Ansel et al., J. Phys. B 57, 133001 (2024).

[2] G. Dridi, K. Liu, S. Guérin, Phys. Rev. Lett. 125, 250403 (2020).

[3] X. Laforgue, G. Dridi, S. Guérin, Phys. Rev. A 106, 052608 (2022).

[4] G. Dridi, X. Laforgue, M. Mejatty, S. Guérin, Phys. Rev. A (2024).

[5] M. Harutyunyan, F. Holweck, D. Sugny, and S. Guérin, Phys. Rev. Lett. 131, 200801 (2023).

[6] K. Liu, D. Sugny, X. Chen, and S. Guérin, Entropy 25, 790 (2023).

[7] J. Zhu and S. Guérin, Control of nonlinear quantum systems: From nonlinear Rabi oscillations to robust two-stage optimal inverse engineering, Phys. Rev. A 110, 063503 (2024).

[8] M. Harutyunyan, B. Peaudecerf, D. Sugny, and S. Guérin, Qubit sensing by optimal narrowband pulses (2025).

[9] C. L. Latune, M. B. Puthuveedu Shebeek, D. Sugny, S. Guérin, Energy shortcut of quantum protocols by optimal control (2025).