All-microwave holonomic control of an electron-nuclear two-qubit register in diamond

Abstract

We present a theoretical scheme that allows one to perform a universal set of holonomic gates on a two-qubit register, formed by a $^{13}\mathrm{C}$ nuclear spin coupled to the electron spin of a nitrogen-vacancy center in diamond. Strong hyperfine interaction between the electron spin and the spins of the first three shells of $^{13}\mathrm{C}$ atoms allows one to operate the state of the register on the submicrosecond timescale using microwave pulses only. We describe the system and the operating regime analytically and numerically, as well as simulate the initialization protocols.