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.

6 pages

References in corpus (4)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
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• Universal extensions of restricted classes of quantum operations

Cited by in corpus (7)

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• Scalable quantum control and non-abelian anyon creation in the Kitaev honeycomb model
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• Quantum speed limit of a single atom in a squeezed optical cavity mode
• Tighter Lower Bounds on Quantum Annealing Times
• Quantum Speed Limits from Symmetries in Quantum Control
• Trajectory-independent speed limits for controlled open quantum systems