State Transfer and Analysis of Quantum Systems on the Bloch Sphere
Shuang Cong · 2014
We begin the basic analysis of system states in a simple two-level quantum system on the Bloch sphere in Chapter 2, including pure states, mixed state expressions, and control trajectory on the Bloch sphere. We also introduce the state transfer of quantum systems on the Bloch sphere by means of geometric control. The Bloch sphere is a suitable tool for presenting a qubit because it gives us an intuitive vision for understanding the physical meanings of quantum bits or variables. In the state transfer of quantum systems on the Bloch sphere, we first present the descriptions of pure states, superposition states, and mixed states. Then we propose the control methods of a single spin-1/2 particle in a Bloch sphere in which we focus on the situations of a minimum control field and a fixed time T. For these two situations, numerical simulations and results analyses are given.