  Rubik's Cube is one of the most famous combinatorial puzzles involving nearly
$4.3 \times 10^{19}$ possible configurations. Its mathematical description is
expressed by the Rubik's group, whose elements define how its layers rotate. We
develop a unitary representation of such group and a quantum formalism to
describe the Cube from its geometrical constraints. Cubies are describedby
single particle states which turn out to behave like bosons for corners and
fermions for edges, respectively. When in its solved configuration, the Cube,
as a geometrical object, shows symmetrieswhich are broken when driven away from
this configuration. For each of such symmetries, we build a Hamiltonian
operator. When a Hamiltonian lies in its ground state, the respective symmetry
of the Cube is preserved. When all such symmetries are preserved, the
configuration of the Cube matches the solution of the game. To reach the ground
state of all the Hamiltonian operators, we make use of a Deep Reinforcement
Learning algorithm based on a Hamiltonian reward. The Cube is solved in four
phases, all based on a respective Hamiltonian reward based on its spectrum,
inspired by the Ising model. Embedding combinatorial problems into the quantum
mechanics formalism suggests new possible algorithms and future implementations
on quantum hardware.
