Accelerating geometric quantum computation through non-cyclic evolution and shortcut to adiabaticity

Realizing fast and robust quantum gates is the key towards realizing fault-tolerance quantum computation. In this paper, we propose to achieve quantum gates based on non-cyclic geometric evolution. Dynamical phase during the evolution is cancelled by spin-echo process and the adiabatic control can be sped up through shortcut to adiabatic manner. Different from geometric gates based on cyclic evolution, the superiority of non-cyclic operation is that the operation time shortens linearly as the rotation angle decreases, which makes the non-cyclic operation more insensitive to the decoherence effect. The proposed scheme is also robust against random noise due to the geometric characteristic of projective Hilbert space. Since the proposed scheme is fast and robust, it may pave a new way to control quantum states efficiently.