关键词：量子算法；线性代数；计算模型；曲线拟合；电流量
摘 要：This dissertation explores several new approaches to developing quantum algorithms. These approaches include span programs, electrical flows and nonsparse Hamiltonian simulation. We demonstrate their power by successfully applying them to some useful problems, including tree detection, effective resistance estimation and curve fitting. All of these algorithms are time-efficient,and some of them are proven to be (nearly) optimal.