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Optimal control of open quantum systems: Theoretical foundations and applications to superconducting quantum devices Koch, Christiane

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Quantum control is an important prerequisite for quantum devices [1]. A major obstacle is the fact that a quantum system can never completely be isolated from its environment. The interaction of a quantum system with its environment causes decoherence. Optimal control theory is a tool that can be used to identify control strategies in the presence of decoherence. I will show how to adapt optimal control theory to quantum information tasks for open quantum systems [2].

A key application of quantum control is to identify performance bounds, for tasks such as state preparation or quantum gate implementation, within a given architecture. One such bound is the quantum speed limit, which determines the shortest possible duration to carry out the task at hand. For open quantum systems, interaction with the environment may lead to a speed-up of the desired evolution. Here, I will show how initial correlations between system and environment may not only be exploited to speed up qubit reset but also to increase state preparation fidelities. Geometric control techniques provide an intuitive understanding of the underlying dynamics [3].

Control tasks such as state preparation or gate implementation are typically optimized for known, fixed parameters of the system. Showcasing the full capabilities of quantum optimal control, I will discuss how recent advances in quantum control techniques allow for going even further. Using a fully numerical quantum optimal control approach, it is possible to map out the entire parameter landscape for superconducting transmon qubits. This allows to determine the global quantum speed limit for a universal set of gates with gate errors limited solely by the qubit lifetimes. It thus provides the optimal working points for a given architecture [4].

While the interaction of qubits with their environment is typically regarded as detrimental, this does not need to be the case. I will show that the back-flow of amplitude and phase encountered in non-Markovian dynamics can be exploited to carry out quantum control tasks that could not be realized if the system was isolated [5]. The control is facilitated by a few strongly coupled, sufficiently isolated environmental modes. These can be found in a variety of solid-state devices including superconducting circuits.

[1] S. Glaser et al.: Training Schrödinger's cat: quantum optimal control, Eur. Phys. J. D 69, 279 (2015)
[2] C. P. Koch: Controlling open quantum systems: Tools, achievements, limitations, J. Phys. Cond. Mat. 28, 213001 (2016)
[3] D. Basilewitsch et al.: Beating the limits with initial correlations, arXiv:1703.04483
[4] M. H. Goerz et al.: Charting the circuit-QED Design Landscape Using Optimal Control Theory, arXiv:1606.08825
[5] D. M. Reich, N. Katz & C. P. Koch: Exploiting Non-Markovianity for Quantum Control, Sci. Rep. 5, 12430 (2015)

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