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Optimal Control

Quantum optimal control is concerned with developing innovative and efficient approaches to manipulate quantum systems. This can be achieved by avoiding adverse effects, such as decoherence or the population of undesired states, and by exploiting numerical optimizations.

Control Problems

Control problems in quantum mechanics may range from manipulating simple systems such as the Landau-Zehner problem [1-2] to complicated many-body arrangements [3]. A control problem can describe the task of steering a quantum system into a particular quantum state or generating a desired unitary transformation.

Solution Techniques

An analytic solution for a (simplified) model of the considered quantum system can be combined with numerical techniques which might be able to include a wider range of features of the system such as noise or non-adiabaticity.

Some Applications

Optimal control is a useful tool in many areas of quantum physics [4]. It has been used to improve the preparation of Bose-Einstein condensates [5], autonomously calibrate nitrogen-vacancy center operations [6] and produce the largest Schrödinger cat state to date (August 2019) using Rydberg atoms [7].

Few Body Systems

RedCRAB (Remote dressed Chopped RAndom Basis algorithm)

RedCRAB is a tool that allows other research groups to easily adopt optimal control in their experiment or simulation. A remote cloud server generates and transmits controls to a local program on a user's computer which then evaluates the control's performance in an experiment or simulation before sending it back to the remote cloud server. In subsequent iterations, the server tends to generate improved controls based on the feedback from the last iteration. Applications can be found in references [4-7].

References

[1] Lloyd, S., & Montangero, S. (2014). Information Theoretical Analysis of Quantum Optimal Control. 113(5), 010502. https://doi.org/10.1103/PhysRevLett.113.010502

[2] Caneva, T., Murphy, M., Calarco, T., Fazio, R., Montangero, S., Giovannetti, V., & Santoro, G. E. (2009). Optimal control at the quantum speed limit. Physical Review Letters, 103(24), 1–4. https://doi.org/10.1103/PhysRevLett.103.240501

[3] Doria, P., Calarco, T., & Montangero, S. (2011). Optimal Control Technique for Many-Body Quantum Dynamics. Physical Review Letters, 106(19), 190501. https://doi.org/10.1103/PhysRevLett.106.190501

[4] Glaser, S. J., Boscain, U., Calarco, T., Koch, C. P., Köckenberger, W., Kosloff, R., Kuprov, I., Burkhard, L., Schirmer, S., Schulte-Herbrüggen, T., Sugny, D., Wilhelm, F. K. (2015). Training Schrödinger’s cat: Quantum optimal control: Strategic report on current status, visions and goals for research in Europe. European Physical Journal D, 69(12), 279. https://doi.org/10.1140/epjd/e2015-60464-1

[5] Heck, R., Vuculescu, O., Sørensen, J. J., Zoller, J., Andreasen, M. G., Bason, M. G., Ejlertsen, P., Elíasson, O., Haikka, P., Laustsen, J.S., Nielsen, L. L., Mao, A., Müller, R., Napolitano, M., Pedersen, M. K., Thorsen, A. R., Bergenholtz, C., Calarco, T., Montangero, S., Sherson, J. F. (2018). Remote optimization of an ultracold atoms experiment by experts and citizen scientists. Proceedings of the National Academy of Sciences of the United States of America, 115(48), E11231. https://doi.org/10.1073/pnas.1716869115

[6] Frank, F., Unden, T., Zoller, J., Said, R. S., Calarco, T., Montangero, S., Naydenov, B., Jelezko, F. (2017). Autonomous calibration of single spin qubit operations. Npj Quantum Information, 3(1), 48. https://doi.org/10.1038/s41534-017-0049-8

[7] Omran, A., Levine, H., Keesling, A., Semeghini, G., Wang, T. T., Ebadi, S., Bernien, H., Zibrov, A. S., Pichler, H., Choi, S., Cui, J., Rossignolo, M., Rembold, P., Montangero, S., Calarco, T., Endres, M., Greiner, M., Vuletić, V.,  Lukin, M. D. (2019). Generation and manipulation of Schrödinger cat states in Rydberg atom arrays. https://doi.org/10.1126/science.aax9743


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