  There is a sub-class of the solutions to Quantum Tetrahedron Equation related
to the algebraical Pentagon Equation. The Quantum Tetrahedron Equation defines
an evolution operator in wholly discrete three dimensional space-time. In this
paper we establish the Liouville integrability of one particular quantum
evolution model/classical integrable model on cubic lattice. The key feature of
the model is that it has two independent quantum/classical spectral curves. In
particular, on the classical level its Hamiltonian equations of motion decouple
into two independent Hirota equations.
