Construction and Implementation of the Geometric Control Theory of Quantum Computing

该项目的主要目的是构建控制量子计算机的几何理论，并通过NMR实验来验证该理论。我们基于李群理论制定了一个减少量子计算执行时间的理论。我们成功地进行了核磁共振实验，证实了我们的理论的适用性。另一方面，退相干已经被认为是在噪声环境中精确控制量子系统的障碍。为了理解退相干的机制，我们提出了人工环境的方法，在人工环境中我们可以产生作用于量子系统的噪声。利用人工环境的方法测量了单量子比特系统的退相干率，并对抑制退相干的bang-bang控制进行了实验。为了更深入地理解退相干，我们还研究了宏观系统中的纠缠和非平衡系统的动力学。特别地，我们证明了在具有亚稳态中间态的量子系统中，弛豫过程变得更快。我们还研究了不确定性关系，微观-宏观二元性，以及它们的信息理论含义。这些研究结果发表在期刊上，并在研讨会上发表。我们组织了暑期学校，鼓励这一领域的年轻科学家。我们还编写了数学物理和量子信息科学的教科书。我们组织了国际研讨会并出版了会议记录。

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.