Orbit Tracking Control of Quantum Systems

TL;DR

This paper presents a control method for orbit tracking in quantum systems by transforming the problem into state transfer using unitary transformations and Lyapunov functions, with proven convergence and simulation validation.

Contribution

It introduces a novel control approach that handles arbitrary initial states and different target state types in quantum orbit tracking using Lyapunov-based control laws.

Findings

Successful control of quantum orbit tracking demonstrated on a two-level system.

Explicit control laws derived for different target state classes.

Simulation results on the Bloch sphere validate the effectiveness of the method.

Abstract

The orbit tracking of free-evolutionary target system in closed quantum systems is studied in this paper. Based on the concept of system control theory, the unitary transformation is applied to change the time-dependent target function into a stationary target state so that the orbit tracking problem is changed into the state transfer one. A Lyapunov function with virtual mechanical quantity P is employed to design a control law for such a state transferring. The target states in density matrix are grouped into two classes: diagonal and non-diagonal. The specific convergent conditions for target state of diagonal mixed-states are derived. In the case that the target state is a non-diagonal superposition state, we propose a non-diagonal P construction method; if the target state is a non-diagonal mixed-state we use a unitary transformation to change it into a diagonal state and design a diagonal P. In such a way, the orbit tracking problem with arbitrary initial state is properly solved. The explicit expressions of P are derived to obtain a convergent control law. At last, the system simulation experiments are performed on a two-level quantum system and the tracking process is illustrated on the Bloch sphere.