  This study combines the quantum Rubik's Cube matrix with the Benalcazar
Bernevig Hughes model, defines a matrix algorithm based on the reverse process
of convolution, and constructs an expression for the quantum Rubik's Cube
matrix and Hamiltonian. Furthermore, in order to make the operation of the
quantum Rubik's Cube matrix clearer, we use a Josephus ring to draw a
topological graph of the Rubik's Cube expansion. This article uses a quantum
Rubik's Cube to calculate energy level transitions of electrons, and shows that
its operation corresponds to path integration. The band dispersion is obtained.
This work provides new ideas and methods for calculating Hamiltonians and
studying energy level structure.
