Construction and Implementation of the Geometric Control Theory of Quantum Computing

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The main purposes of this project are to construct a geometric theory for controlling quantum computers and to test the theory by NMR experiments. We formulated a theory for reducing execution times of quantum computing based on the Lie group theory. We successfully peck wed an NMR experiment and confirmed the applicability of our theory. On the other hand, decoherence has been known as an obstacle against accurate control of a quantum system in a noisy environment. For understanding the mechanism of decoherence we proposed the method of artificial environment, in which we can generate noises acting on the quantum system. Using the method of artificial environment we measured the decoherence rate of a one-qubit system and tested the bang-bang control, which suppressed the decoherence. To get a deeper understanding of decoherence we also studied entanglement in macroscopic systems and dynamics of non-equilibrium systems. In particular, we showed that the relaxation process becomes faster in a quantum system which has a metastable intermediate state. We studied also the uncertainty relation, the micro-macro duality, and their information theoretical implications. These results were published in journals and presented at workshops.We organized summer school to encourage young scientists in this field. We also wrote textbooks on mathematical physics and on quantum information science. We organized international workshops and published proceedings.