Improved error thresholds for measurement-free error correction

Understand

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.