Solving Rubik’s cube via quantum mechanics and deep reinforcement learning

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