Trap-free manipulation in the Landau-Zener system

TL;DR

This paper proves that the Landau-Zener quantum system is free of traps for certain control tasks, providing a rare example of a fully trap-free controlled quantum system, with implications for practical quantum control under constraints.

Contribution

It demonstrates the absence of traps in the Landau-Zener system for key control tasks, solving a longstanding open problem in quantum control theory.

Findings

Landau-Zener system is trap-free for transition probability and unitary gate control

Laboratory constraints can induce traps under severe conditions

First example of a controlled quantum system completely free of traps

Abstract

The analysis of traps, i.e., locally but not globally optimal controls, for quantum control systems has attracted a great interest in recent years. The central problem that has been remained open is to demonstrate for a given system either existence or absence of traps. We prove the absence of traps and hence completely solve this problem for the important tasks of unconstrained manipulation of the transition probability and unitary gate generation in the Landau-Zener system---a system with a wide range of applications across physics, chemistry and biochemistry. This finding provides the first example of a controlled quantum system which is completely free of traps. We also discuss the impact of laboratory constraints due to decoherence, noise in the control pulse, and restrictions on the available controls which when being sufficiently severe can produce traps.