Experimental quantum error correction with high fidelity

TL;DR

This paper demonstrates improved quantum error correction using advanced control techniques like GRAPE pulses, achieving higher fidelity and maintaining advantages despite additional operational errors.

Contribution

It reproduces and enhances previous QEC experiments by applying modern control methods, significantly improving fidelity and robustness.

Findings

Enhanced QEC fidelity with GRAPE pulses

Maintained error correction advantage despite added operations

Reproduced and improved upon previous NMR QEC results

Abstract

More than ten years ago a first step towards quantum error correction (QEC) was implemented [Phys. Rev. Lett. 81, 2152 (1998)]. The work showed there was sufficient control in nuclear magnetic resonance (NMR) to implement QEC, and demonstrated that the error rate changed from $\epsilon$ to approximatively $\sim\epsilon^2$. In the current work we reproduce a similar experiment using control techniques that have been since developed, such as GRAPE pulses. We show that the fidelity of the QEC gate sequence, and the comparative advantage of QEC are appreciably improved. This advantage is maintained despite the errors introduced by the additional operations needed to protect the quantum states.