Quantum control with a multi-dimensional Gaussian quantum invariant

Selwyn Simsek and Florian Mintert

Physics Department, Blackett Laboratory, Imperial College London, Prince Consort Road, SW7 2BW, United Kingdom

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The framework of quantum invariants is an elegant generalization of adiabatic quantum control to control fields that do not need to change slowly. Due to the unavailability of invariants for systems with more than one spatial dimension, the benefits of this framework have not yet been exploited in multi-dimensional systems. We construct a multi-dimensional Gaussian quantum invariant that permits the design of time-dependent potentials that let the ground state of an initial potential evolve towards the ground state of a final potential. The scope of this framework is demonstrated with the task of shuttling an ion around a corner which is a paradigmatic control problem in achieving scalability of trapped ion quantum information technology.

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Cited by

[1] Kazutaka Takahashi, "Dynamical invariant formalism of shortcuts to adiabaticity", Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 380 2239, 20220301 (2022).

[2] Ander Tobalina, Juan Gonzalo Muga, Ion Lizuain, and Mikel Palmero, "Shortcuts to adiabatic rotation of a two-ion chain", Quantum Science and Technology 6 4, 045023 (2021).

[3] Modesto Orozco-Ruiz, Selwyn Simsek, Sahra A. Kulmiya, Samuel J. Hile, Winfried K. Hensinger, and Florian Mintert, "Optimal control with a multidimensional quantum invariant", Physical Review A 108 2, 022601 (2023).

[4] Omar Raii, Florian Mintert, and Daniel Burgarth, "Scalable quantum control and non-Abelian anyon creation in the Kitaev honeycomb model", Physical Review A 106 6, 062401 (2022).

[5] Xiao-Jing Lu, Ion Lizuain, and J. G. Muga, "Inverse engineering of fast state transfer among coupled oscillators", Quantum 6, 740 (2022).

[6] Xiao-Jing Lu, Mikel Palmero, Ion Lizuain, and Juan Gonzalo Muga, "Fast Driving of a Particle in Two Dimensions without Final Excitation", Entropy 24 11, 1694 (2022).

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