Graph isomorphism and quantisation of longest cycles by means of determinants and spectra

描述哈密尔顿循环问题和图同构问题的困难将是一个重要的概念性进步，在许多领域产生影响，包括组合优化和理论计算机科学，特别是Google PageRank。张量网络技术的应用将导致量子计算机的设计，枚举图中的所有哈密尔顿圈。分析行列式目标函数的特征值，可以得到随机矩阵新的谱性质。利用这种特性的化学进步将大大有助于解决广泛应用中的问题的现有技术。

A characterisation of the difficulty of the Hamiltonian cycle problem and the graphs isomorphism problem will be a significant conceptual advancement with repercussions in a number of fields including combinatorial optimisation and theoretical computer science, in particular, the Google PageRank. Applications of tensor networks technique will lead to a design of a quantum computer that enumerates all Hamiltonian cycles in a graph. Analysis of the determinant objective function in terms of the eigenvalues may lead to new spectral properties of stochastic matrices. Algorithmic advances exploiting such a characterisation will significantly contribute to existing technologies for solving problems in a wide range of applications.