Complete leakage removal in the surface code on superconducting qubits - Part 1

Quantum error correction can suppress errors only when they are sufficiently uncorrelated. During computation, unused higher energy levels of superconducting qubits can become excited, creating leakage states that are long-lived and mobile. These states induce a large number of correlated error detections, playing an outsized role in producing logical errors. Further, the population accumulates in these states as the code is extended in time, and is a limiting factor in cutting-edge QEC experiments. Here, we study the dynamics of such leakage events in the context of the surface code error correction circuit, showing how leakage spreads in space and time. Finally, we summarize the state of the art in the impact of leakage on cutting-edge surface code experiments.