Quantum speed problem: Theoretical hints for control

Abstract

The transition time between states plays an important role in designing quantum devices as they are very sensitive to environmental influences. Decoherence phenomenon is responsible for possible destructions of the entanglement that is a fundamental requirement to implement quantum information processing systems. If the time between states is minimized, the decoherence effects can be reduced, thus, it is advantageous to the designer to develop expressions for time performance measures. Quantum speed limit (QSL) problem has been studied from the theoretical point of view, providing general results. Considering the implementation of quantum control systems, as the decoherence phenomenon is unavoidable, it is important to apply these general results to particular cases, developing expressions and performance measures, to assist control engineering designers. Here, a minimum time performance measure is defined for quantum control problems, for time-independent or time-dependent Hamiltonians, and applied to some practical examples, providing hints that may be useful for researchers pursuing optimization strategies for quantum control systems.

Minimum Time in Quantum State Transitions: Dynamical Foundations and Applications

“…where t min is the shortest physically possible time to obtain a desired transition of quantum states, and t CQS is the time by which such transition can be effectively accomplished in the controlled quantum system, hence, the notation chosen is [8].…”

“…Thereafter, we wish to apply the Mandelstam-Tamm timeenergy inequality to a quantum system of interest, for example, the Fahri-Gutmann model of digital quantum computation [7], in order to obtain an analytical expression for the minimal time required for a state transition in such a quantum system. These analyses allow us to ultimately introduce a quantitative measure for the performance of time-optimal quantum controls [8].…”

“…In[8], we present an analytical case study of a time-dependent Hamiltonian, namely the Landau-Zener system.Research Advances in Quantum Dynamics…”