Probing the ultra-low error regime with repetition codes

Despite recent realizations of below-threshold surface codes, orders of magnitude remain between present logical error rates and the requirements for practical quantum computation. High-distance repetition codes only protect one degree of freedom, but enable the exploration of the ultra-low-error regime of quantum error-correction performance. We run repetition codes up to distance-29 and observe an error suppression factor of Λ = 8.4±0.1, achieving a logical error per cycle around 10⁻¹⁰, four orders of magnitude better than previous results. However, we find that logical performance is limited by rare correlated error events occurring approximately once every hour, or 3×10⁹ cycles, setting a floor around 10⁻¹⁰. These unexpected correlated errors raise concerns for the eventual ultra-low error performance of the surface code and may preclude larger fault-tolerant circuits. We present an analysis of the different failure modes that lead to logical error, and experimental progress towards understanding the cause of these events.