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Quantum Control by the Environment: Turing Uncomputability, Optimization over Stiefel Manifolds, Reachable Sets, and Incoherent GRAPE

  • QUANTUM INFORMATICS: COMPUTING
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Abstract

The ability to control quantum systems is necessary for many applications of quantum technologies ranging from gate generation in quantum computation to NMR and laser control of chemical reactions. In many practical situations, the controlled quantum systems are open, i.e., interacting with the environment. While often influence of the environment is considered as an obstacle for controlling the systems, in some cases it can be exploited as a useful resource. In this note, we briefly review some results on control of open quantum systems using environment as a resource, including Turing uncomputability of discrete quantum control, parametrization of Kraus maps by points of the Stiefel manifolds and corresponding Riemanninan optimization, control by dissipation and time-dependent decoherence rates, reachable sets, and incoherent GRAPE (Gradient Ascent Pulse Engineering) for gradient-based optimization.

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Notes

  1. Sometimes not-completely positive dynamics is also considered [13, 14], but here we do not consider this case.

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This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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  1. Department of Mathematical Methods for Quantum Technologies, Steklov Mathematical Institute, Russian Academy of Sciences, 119991, Moscow, Russia

    A. N. Pechen

  2. Quantum Engineering Research and Education Center, University of Science and Technology MISIS, 119991, Moscow, Russia

    A. N. Pechen

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Pechen, A.N. Quantum Control by the Environment: Turing Uncomputability, Optimization over Stiefel Manifolds, Reachable Sets, and Incoherent GRAPE. Russ Microelectron 52 (Suppl 1), S419–S423 (2023). https://doi.org/10.1134/S1063739723600826

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