论文标题
量子与古典马尔可夫连锁店；确切可解决的示例
Quantum vs classical Markov chains; Exactly solvable examples
论文作者
论文摘要
提出了图形上一般可逆的马尔可夫链的无符合定量程序。通过根据可逆分布的平方根对基本过渡概率矩阵K的相似性转换获得了量子Hamiltonian H。经典和量子马尔可夫链的演变是通过基于ASKEY方案的高几何正交多项式的大约二十张Quantum Hamiltonian H的本征值问题的解决方案来描述的。其中有五个明确的例子与Krawtchouk，Hahn，Q-Hahn，Charlier和Meixner有关，以说明实际计算。
A coinless quantisation procedure of general reversible Markov chains on graphs is presented. A quantum Hamiltonian H is obtained by a similarity transformation of the fundamental transition probability matrix K in terms of the square root of the reversible distribution. The evolution of the classical and quantum Markov chains is described by the solutions of the eigenvalue problem of the quantum Hamiltonian H. About twenty plus exactly solvable Markov chains based on the hypergeometric orthogonal polynomials of Askey scheme, derived by Odake-Sasaki, would provide a good window for scrutinising the quantum/classical contrast of Markov chains. Among them five explicit examples, related to the Krawtchouk, Hahn, q-Hahn, Charlier and Meixner, are demonstrated to illustrate the actual calculations.
