Realistic numerical simulation of a distance-3 surface code implemented on a superconducting chip

The surface code is an appealing candidate for quantum error correction because of its relatively high threshold and the locality of the interactions needed to perform syndrome measurements. In this talk, we study the performance of small surface codes implemented on transmon-based superconducting processors with realistic time-domain numerical simulations. More precisely, we investigate the memory fidelity of a near-term implementation of a distance-3 surface code by characterizing the logical error channel as a function of device parameters. Our analysis focuses on the interplay between the effects of decoherence and spurious cross-Kerr interactions on the error rate of the logical qubit.