Holonomic Quantum Computation via Adiabatic Shortcut

Fast quantum gates based on geometric phases provide a platform for performing robust quantum computation. In particular, non-adiabatic holonomic quantum computation, which involves non-Abelian geometric phases to achieve universality, has recently been demonstrated in several experiments. Here, we generalize the transitionless quantum driving algorithm to a degenerate Hilbert space, with which we propose a route towards fast holonomic quantum computation. We propose a proof-of-principle experiment in a superconducting circuit architecture to realize our scheme.