论文标题
线性代数和量子算法
Linear algebra and quantum algorithm
论文作者
论文摘要
在数学方面，我们介绍了量子算法和量子计算机的数学结构。量子算法在有限的尺寸复杂内部产品空间上通过线性代数表示。 von Neumann于1930年左右建立了量子力学的数学公式。该公式使用功能分析，线性代数和概率理论。 QM的数学公式的知识是足够的量子机械知识，可以接近量子算法，对于从QM的数学公式开始的数学家来说，这可能是有效的方法。我们短暂地解释了量子力学的数学公式，量子位，量子门，量子离散的傅立叶变换，Deutsch的算法和Shor的算法。
In mathematical aspect, we introduce quantum algorithm and the mathematical structure of quantum computer. Quantum algorithm is expressed by linear algebra on a finite dimensional complex inner product space. The mathematical formulations of quantum mechanics had been established in around 1930, by von Neumann. The formulation uses functional analysis, linear algebra and probability theory. The knowledge of the mathematical formulation of QM is enough quantum mechanical knowledge for approaching to quantum algorithm and it might be efficient way for mathematicians that starting with mathematical formulations of QM. We explain the mathematical formulations of quantum mechanics briefly, quantum bits, quantum gates, quantum discrete Fourier transformation, Deutsch's algorithm and Shor's algorithm.
