Long-range photon-mediated gate scheme between nuclear spin qubits in diamond

TL;DR

This paper proposes a fast, cavity-mediated scheme for implementing a universal two-qubit gate between distant nuclear spin qubits in diamond, leveraging virtual photon exchange via optical cavities.

Contribution

It introduces a novel cavity-based method to entangle and perform gates between remote nuclear spins in diamond, achieving operation times much shorter than decoherence times.

Findings

Operation times below 100 nanoseconds predicted.

The scheme enables a universal controlled-Z gate between nuclear spins.

The approach is several orders of magnitude faster than nuclear spin decoherence.

Abstract

Defect centers in diamond are exceptional solid-state quantum systems that can have exceedingly long electron and nuclear spin coherence times. So far, single-qubit gates for the nitrogen nuclear spin, a two-qubit gate with a nitrogen-vacancy (NV) center electron spin, and entanglement between nearby nitrogen nuclear spins have been demonstrated. Here, we develop a scheme to implement a universal two-qubit gate between two distant nitrogen nuclear spins. Virtual excitation of an NV center that is embedded in an optical cavity can scatter a laser photon into the cavity mode; we show that this process depends on the nuclear spin state of the nitrogen atom. If two NV centers are simultaneously coupled to a common cavity mode and individually excited, virtual cavity photon exchange can mediate an effective interaction between the nuclear spin qubits, conditioned on the spin state of both nuclei, which implements a universal controlled-$\textit{Z}$ gate. We predict operation times below 100 nanoseconds, which is several orders of magnitude faster than the decoherence time of nuclear spin qubits in diamond.