线性代数与量子算法

摘要：

在数学方面，介绍了量子算法和量子计算机的数学结构。量子算法在有限维复内积空间上用线性代数表示。量子力学的数学公式是在1930年左右由冯·诺依曼建立的。该公式使用泛函分析，线性代数和概率论。量子力学的数学表述是研究量子算法的足够的量子力学知识，从量子力学的数学表述入手可能是数学家研究量子算法的有效途径。简要介绍了量子力学的数学表述，量子比特、量子门、量子离散傅里叶变换、Deutsch算法和Shor算法。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。