Improved error thresholds for measurement-free error correction

TL;DR

This paper demonstrates that measurement-free quantum error correction, utilizing redundant syndrome extraction and multi-qubit gates, can achieve error thresholds comparable to or better than measurement-based methods, advancing practical quantum computing.

Contribution

It introduces a measurement-free error correction protocol with enhanced fault tolerance by extracting redundant syndrome information, suitable for neutral atom qubits.

Findings

Threshold error rates of 10^{-3} to 10^{-4} achieved

Coherent error correction outperforms previous schemes

Multi-qubit gates improve fault tolerance

Abstract

Motivated by limitations and capabilities of neutral atom qubits, we examine whether measurement-free error correction can produce practical error thresholds. We show that this can be achieved by extracting redundant syndrome information, giving our procedure extra fault tolerance and eliminating the need for ancilla verification. The procedure is particularly favorable when multi-qubit gates are available for the correction step. Simulations of the bit-flip, Bacon-Shor, and Steane codes indicate that coherent error correction can produce threshold error rates that are on the order of $10^{-3}$ to $10^{-4}$---comparable with or better than measurement-based values, and much better than previous results for other coherent error correction schemes. This indicates that coherent error correction is worthy of serious consideration for achieving protected logical qubits.