Quantum Computing and Optimal Control Theory

Abstract

In recent years, quantum computing and quantum information science have become one of the most important and attractive research areas in a variety of disciplines, e. g., mathematics, information science, physics, chemistry, etc1. These new kinds of technologies are predicted to be much more advantageous compared with the classical computers and classical information science and the benefit obtained by these technologies is assumed to be beyond measure in our every-day life. For instance, quantum computers are predicted to be able to solve mathematical problems that today’s fastest computers could not solve in years. In particular, entanglement or entangled state plays a key role for quantum computing and quantum information processing. For example, arbitrary quantum states of two-level system can be teleported through classical communication with the help of maximally entangled Bell state from one place to other macroscopic distant places (quantum teleportation)2, which has no counterpart in classical mechanics. As opposed to the quantum teleportation, classical information can be teleported by using the maximally entangled Bell state (superdense coding)3. Needless to say, entanglement is also an essential ingredient in quantum computing1. At present, theoretical investigations of the mechanism of quantum computing and quantum information science have become mature although some of the important theoretical problems, e. g., definition of entanglement degree of multipartite systems, have not yet been solved and are still controversial. Yet, one can say that we are now reaching a stage of experimental realizations of quantum computing and quantum information processing proposed and investigated theoretically and numerically. To apply quantum computing and quantum information processing to realistic quantum systems, a number of microscopic quantum systems have been proposed. Just to mention a few, cavity quantum electrodynamics (cavity QED)4, trapped ions5 7, neutral atoms trapped in optical lattices8, nuclear magnetic resonance (NMR)9, 10, superconducting circuits11, silicon-based nuclear spin12, diamond-based quantum computer13, 14 are some of the promising candidates of quantum computing devices. However, investigation of utilization of molecular internal degrees of freedom for quantum computing and quantum information science, in particular, electronic, vibrational, and rotational degrees of freedom, is still in its infancy. Although molecules are also quantum systems, very few chemists have yet examined how to use molecular internal degrees of