Quantum Distance to Uncontrollability and Quantum Speed Limits

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.

arXiv comment6 pages

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• Tighter Lower Bounds on Quantum Annealing Times
• Quantum Speed Limits from Symmetries in Quantum Control
• Trajectory-independent speed limits for controlled open quantum systems