Invariant-based inverse engineering for fast nonadiabatic geometric quantum computation

Abstract

In this paper, based on first given Lewis–Riesenfeld invariant depicted by a unit vector in parameter space, we inverse engineering the time-dependent Hamiltonian of a system with su(2) Lie algebraic structure. The introduced method is then applied to investigate nonadiabatic Abelian geometric quantum computation. We demonstrate that, by employing the nonadiabatic Berry phase generated through nonadiabatic periodic evolution, a driven two-level system which undergoes a single cyclic evolution along a loop path in Bloch space can realize a universal set of one-qubit gates. Subsequently, under consideration of the influence of the systematic error and dissipation on nonadiabatic process, the result reveals arbitrary one-qubit gate can be implemented with a high fidelity. Moreover, to complete the universal set, arbitrary controlled-U gate is designed by utilizing a driven system consisted of a pair of coupled spin subsystems.