In this seminar, we plan to learn basics and esstentials of mathematics in quatum computing, following the “bible”: Chuang-Nielson, Quantum Computation and Quantum Information, 10th Anniversary Edition. After the invention of quantum physics, the existence of a quantum computer is suggested by physicists in 1970’s, such as in R. Feyman’s 1982 paper, and people have tried to exploit its computational power. Though many quantum algorithm have been developeds, cf. Quantum Algorithm Zoo, many of them are still inapplicable due to the lack of suitable hardware. Nonetheless, finding more quantum algorithms or modeling problems in quantum computation remain to be big challenges and have potential effect to future life, see 台灣發展量子計算科技產業的策略(2020/5).