Quantum control of nuclear magnetic resonance spin systems

Abstract

With the development of quantum information science, the active manipulation of quantum systems is becoming an important research frontier. To build realistic quantum information processors, one of the challenges is to implement arbitrary desired operations with high precision on quantum systems. A large number of quantum control methods and relevant numerical techniques have been put forward in recent years, such as quantum optimal control and quantum feedback control. Nuclear magnetic resonance (NMR) spin systems offer an excellent testbed to develop benchmark tools and techniques for controlling quantum systems. In this review paper, we briefly introduce some of the basic control ideas developed for NMR systems in recent years. We first explain, for the liquid spin systems, the physics of various couplings and the causes of relaxation effects. These mechanisms govern the system dynamics, and thus are crucial for constructing rigorous and efficient control models. We also identify three types of available control means: 1) raido-frequency fields as coherent controls; 2) phase cycling, gradient fields and relaxation effects as non-unitary controls; 3) radiation damping effect as feedback control mechanism. Then, we elucidate some important control tasks, which may arise from the conventional NMR spectroscopy (e.g., pulse design and polarization transfer) or from quantum information science (e.g., algorithmic cooling and pseudo-pure state preparation). In the last part, we review some of the most important control methods that are applicable to NMR control tasks. For systems with a relatively small number of spins, it is possible to use analytic optimal control theory to realize the target unitary operations. However, for larger systems, numerical methods are necessary. The gradient ascent pulse engineering algorithm and pulse compiler techniques are the most successful techniques for implementing complicated quantum networks currently. There are some interesting topics of utilizing radiation damping and relaxation effects to achieve more powerful controls. Finally, we give an outline of the possible future work.