Detection and mitigation of leakage in simulations of a transmon implementation of the surface code, Part 2: Scalable Hidden Markov models for the identification of leakage*

The detection and mitigation of leakage, a threatening error source for stabilizer quantum error correction (QEC) on leading physical hardware, is an important step towards demonstrations of fault tolerance. We explore the effects of leakage on the performance of the distance-3 surface code Surface-17 by performing density-matrix simulations, employing realistic error models for transmon qubits in a circuit QED processor. We demonstrate the indirect detection of leakage via a network of local, independent and scalable Hidden Markov models. We show that post-selecting on detection of leakage restores the logical fidelity of the encoded information. We explore the integration of leakage detection into a minimum-weight perfect-matching decoder.