Quantum Distance to Uncontrollability and Quantum Speed Limits

TL;DR

This paper introduces a quantum analogue of the classical distance to uncontrollability, providing a geometric and dynamical decomposition of quantum speed limits, with applications to solid state qubits and cross-Kerr systems.

Contribution

It defines Quantum Distance to Uncontrollability and links it to quantum speed limits, offering a new quantitative tool for quantum system design and analysis.

Findings

Quantum Distance to Uncontrollability quantifies proximity to non-universal systems.

Decomposition of quantum speed limits into geometric and dynamical parts.

Application to physical systems reveals insights into spectral crowding and interaction bottlenecks.

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.