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arXiv · 2010.16156

Quantum Distance to Uncontrollability and Quantum Speed Limits

Daniel Burgarth·Jeff Borggaard·Zoltán Zimborás
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Abstract

Distance to Uncontrollability is a crucial concept in classical control theory. Here, we introduce Quantum Distance to Uncontrollability as a measure how close a universal quantum system is to a non-universal one. This allows us to provide a quantitative version of the Quantum Speed Limit, decomposing the bound into a geometric and dynamical component. We consider several physical examples including globally controlled solid state qubits and a cross-Kerr system, showing that the Quantum Distance to Uncontrollability provides a precise meaning to spectral crowding, weak interactions and other bottlenecks to universality. We suggest that this measure should be taken into consideration in the design of quantum technology.

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Daniel Burgarth, Jeff Borggaard, Zoltán Zimborás. 2020-10-30. Quantum Distance to Uncontrollability and Quantum Speed Limits. https://doi.org/10.1103/physreva.105.042402

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