Randomized compiling in fault-tolerant quantum computation

Understand

Studies of quantum error correction (QEC) typically focus on stochastic Pauli errors because the existence of a threshold error rate below which stochastic Pauli errors can be corrected implies that there exists a threshold below which generic errors can be corrected.

• However, rigorous estimates of the threshold for generic errors are typically orders of magnitude worse than the threshold for stochastic Pauli errors.
• Specifically, coherent errors have a particularly harmful impact on the encoded space because they can map encoded states to superpositions of logical and error states.
• Further, coherent errors can add up and interfere over multiple rounds of error correction or between syndrome measurements, which may result in significantly worse errors than expected under a stochastic Pauli error model.