Universal quantum control over Majorana zero modes

Abstract

Majorana zero mode (MZM) exhibits inherent resilience to local parametric fluctuations, due to the topological protection mechanism in the non-Abelian braiding statistics of the anyonic quasiparticles. In this paper, we construct the braiding operations between an arbitrary pair in three MZMs under the theoretical framework of universal quantum control. Largely detuned driving fields on the mediator, a local defect of lattice, enable indirect and tunable exchange interaction between arbitrary two MZMs. The braiding operations can then emerge through the time evolution along the universal nonadiabatic passages, whose robustness against driving-field errors and quasiparticle poisoning can be substantially enhanced by the rapid modulation over the passage-dependent global phase. Moreover, a chiral transfer for population on MZMs along the universal passage can be perfectly demonstrated in both clockwise and counterclockwise manners without eliminating the mediator defect. Our protocol is linear scalable and provides an avenue towards the universal quantum control over MZMs, which is fundamental and essential for topological quantum computation.