Optimal control of fast and high-fidelity quantum gates with electron and nuclear spins of a nitrogen-vacancy center in diamond

TL;DR

This paper demonstrates that quantum optimal control theory can be used to design fast, high-fidelity quantum gates for NV center-based qubits, surpassing fault-tolerance thresholds despite system noise and leakage effects.

Contribution

It introduces a control scheme using the Krotov method to optimize quantum gates in NV centers, achieving error rates below fault-tolerance thresholds.

Findings

High-fidelity single and two-qubit gates achieved

Errors below fault-tolerance thresholds demonstrated

Effective control despite leakage and noise effects

Abstract

A negatively charged nitrogen vacancy (NV) center in diamond has been recognized as a good solid-state qubit. A system consisting of the electronic spin of the NV center and hyperfine-coupled nitrogen and additionally nearby carbon nuclear spins can form a quantum register of several qubits for quantum information processing or as a node in a quantum repeater. Several impressive experiments on the hybrid electron and nuclear spin register have been reported, but fidelities achieved so far are not yet at or below the thresholds required for fault-tolerant quantum computation (FTQC). Using quantum optimal control theory based on the Krotov method, we show here that fast and high-fidelity single-qubit and two-qubit gates in the universal quantum gate set for FTQC, taking into account the effects of the leakage state, nearby noise qubits and distant bath spins, can be achieved with errors less than those required by the threshold theorem of FTQC.