Experimentally Probing Time-like Errors in Quantum Error Correction with Surface Code Stability Circuits (Part 1)

Fault-tolerant algorithms in Quantum Error Correction (QEC) rely on topological operations that involve two key tasks: maintaining logical observables over time, and transporting them through space. While memory experiments typically assess QEC's effectiveness by measuring the preservation of logical observables over time, a complementary approach, the stability experiment, evaluates the successful transfer of logical observables across space [Gidney 2022]. It's crucial to note that preserving logical observables across space has different susceptibilities to physical errors compared to preserving them in time. Specifically, stability experiments are more sensitive to error mechanisms that result in errors extending over multiple QEC cycles, which we term "time-like error chains." These mechanisms encompass device instabilities, leakage to non-computational states, and other time-correlated error sources.

This two-part presentation examines the performance of QEC stability experiments on Google Quantum AI's Willow processors, developing a thorough error model to interpret the results. Part 1 will delve into the theoretical underpinnings of the stability experiment, the error model's construction, and the methodology for efficient simulations.