Non-Abelian Shortcuts to Adiabaticity Simulated by Classical Resonant Oscillators

Quantum degenerate systems can be simulated by the classical resonant oscillators in the means of quantum-classical mapping theory. In this work, we show the classical version of shortcuts to adiabaticity-transitionless quantum driving (TQD) for the non-Abelian quantum systems by averaging the quantum version. The non-Abelian geometric angle corresponding to the quantum Wilczek-Zee phase is given and the non-Abelian angle gauge potential is just the opposite of the third term of TQD Hamiltonian or the averaging of Wilczek-Zee gauge potential. An example of Hamiltonian with two degenerate subspaces is employed to illustrate the classical non-Abelian dynamics, geometric angle and shortcuts to adiabaticity. This provides a promising platform to simulate the quantum shortcut or for quantum computation and quantum information processing.