  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 are 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.
