Controlling quantum spins

Andreas P. Sandiwan, Adha Imam Cahyadi, Samiadji Herdjunanto

Theoretical study on the control of spin-1/2 quantum system is an important matter for the development of quantum control theory. Lyapunov methods play vital role in quantum control because of their concise mathematical rigor. Previously, using the Lyapunov methods, it has been shown that signum function control law can be employed to control spin-1/2 quantum system to achieve NOT quantum gate operation. This paper demonstrates that other forms of control law can be used to control spin-1/2 quantum system to achieve the same NOT quantum gate operation. Two examples of those other forms are provided, namely hyperbolic tangent (tanh) function and proportional multiplier. It is also explained why signum function is not the only function that can be used to control spin-1/2 quantum system. This paper also shows the advantage of using fully-differentiable control law instead of signum function, which is not fully-differentiable. Control law design and stability analysis are conducted using Lyapunov methods. The numerical simulation results show that tanh and proportional multiplier function can also control spin-1/2 quantum system and achieve the NOT quantum gate operation.

Dwight R. Luhman

Jincheng Zhang

Quantum spin is a fascinating and weakly interacting quantum system with unique properties, including the ability to exhibit topological phases. These topological phases possess inherent robustness against local perturbations, making them valuable for quantum information processing and quantum technologies. This paper explores the application of quantum spin to adaptive topology control, proposing a novel method leveraging the self-adaptative nature of quantum spin to dynamically adjust the structure of a quantum system, thereby enabling precise control and optimization. Quantum spin provides a unique platform for exploring novel control strategies, potentially surpassing traditional approaches in terms of accuracy and robustness. The proposed method focuses on utilizing the inherent topological properties of quantum spin to achieve precise manipulation of quantum states. The core claim is that a tailored control mechanism, operating on the self-adaptative behavior of quantum spin, can lead to more precise control of quantum systems. This work addresses the limitations of current control techniques and introduces a fundamentally new approach to topology control.

Vinitha Balachandran, Jiangbin Gong

Controlled measurement processes with high fidelity and robustness will be of substantial interest to fundamental quantum studies as well as quantum-information processing. This work proposes a simple scheme to realize controlled measurements of the state of a single spin, via controlled quantum signal amplification in a one-dimensional spin-chain model. It is shown that, by adiabatically moving an external field applied to a spin chain that is also irradiated with a transverse driving field, a robust spin amplifier may be realized with little dispersion. Our results may find applications in spin-based quantum-information processing and in controlled growth of ``Schr\"odinger cat'' states.

Jianpei Geng