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

TL;DR

This paper proposes a theoretical scheme for universal holonomic quantum gates on a two-qubit system in diamond, utilizing microwave control of electron and nuclear spins with strong hyperfine interaction.

Contribution

It introduces a novel all-microwave method for holonomic control of a two-qubit register in diamond, combining analytical, numerical, and simulation approaches.

Findings

Achieves submicrosecond gate operations using microwave pulses.

Demonstrates the feasibility of holonomic control in a diamond-based two-qubit system.

Provides detailed system analysis and initialization protocols.

Abstract

We present a theoretical scheme that allows to perform a universal set of holonomic gates on a two qubit register, formed by a $^{13}$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 $^{13}$C atoms allows 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.