Detection and mitigation of leakage in simulations of a transmon implementation of the surface code, Part 1: Characterization of leakage effects in a realistic error model

Qubit leakage is present in leading quantum computing platforms, including superconducting transmon qubits. These errors fall outside the stabilizer formalism of quantum error correction (QEC), thus constituting a threatening error source for fault tolerance. While the performance of QEC codes, such as the surface code, has been investigated for simplistic leakage error models, an analysis with respect to a physically-motivated leakage error model for transmons has not been undertaken so far. In this work, we employ realistic full-trajectory simulations of the CZ gate in a transmon system (the dominant source of leakage in this system). We find novel effects within the leakage subspace of two transmons, including leakage mobility and leakage conditional phases. We use this in density-matrix simulations of the distance-3 surface code Surface-17 and study the leakage build-up, its lifetime, and how leaked qubits spread errors onto neighboring qubits.