Low-Depth Flag-Style Syndrome Extraction for Small Quantum Error-Correction Codes

Understand

Flag-style fault-tolerance has become a linchpin in the realization of small fault-tolerant quantum-error correction experiments.

• The flag protocol's utility hinges on low qubit overhead, which is typically much smaller than in other approaches.
• However, as in most fault-tolerance protocols, the advantages of flag-style error correction come with a tradeoff: fault tolerance can be guaranteed, but such protocols involve high-depth circuits, due to the need for repeated stabilizer measurements.
• Here, we demonstrate that a dynamic choice of stabilizer measurements, based on past syndromes, and the utilization of elements from the full stabilizer group, leads to flag protocols with lower-depth syndrome-extraction circuits for the [[5,1,3]] code, as well as for the Steane code when compared to the standard methods in flag fault tolerance.