AI 中文总结
该论文研究了实数与复数Hadamard矩阵的TSS图，发现复数矩阵引入相位并产生非均匀概率，可用于无需手动参数化的振幅放大，且图几乎同构，对量子算法开发有潜在价值。
AI 中文摘要
我们观察到，无论是实数还是复数Hadamard矩阵，对于任何给定的单一输入态，都会产生相同概率的密集输出。复数Hadamard矩阵具有不寻常的阶数并引入相位，这在受控相位变换门的使用中被证明是有用的。通过取输入态的叠加组合，我们发现Hadamard矩阵产生非均匀概率，这对于无需像Grover算子那样手动参数化的振幅放大具有实际意义。我们将多种图论性质应用于TSS图，并探讨了它们的趋势。此外，对于相同的输入态集合，图几乎是同构的，这对开发量子算法具有潜在应用。关键词：量子算法，Hadamard矩阵，酉矩阵方法，叠加的拓扑结构（TSS），图论。
英文摘要
We have observed that Hadamard matrices whether real or complex lead to a dense output of identical probabilities for any given single input state. Complex Hadamard matrices have unusual orders and introduce phase which prove useful when controlled phase transformation gates are used. By taking a superposed combinations of input states, we discovered that the Hadamards generate non-uniform probabilities which is practically significant towards amplitude amplification without the need for manual parameterization like Grover's operator~\cite{grover1996}. A variety of graph theoretic properties are applied to TSS graphs and their trends were explored. Additionally, graphs turn out to be nearly isomorphic for the same set of input states which has potential applications for developing Quantum Algorithms. Keywords: Quantum Algorithms, Hadamard Matrices, Unitary Matrix Approach, Topological Structure of Superpositions (TSS), Graph Theory
Commentsfixed typo in table 1, page 4, two entries came out empty in the v0 submission
