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We present a full density-matrix simulation of the quantum memory andcomputing performance of the distance-3 logical qubit Surface-17, following arecently proposed quantum circuit and using experimental error parameters fortransmon qubits in a planar circuit QED architecture. We use this simulation tooptimize components of the QEC scheme (e.g., trading off stabilizer measurementinfidelity for reduced cycle time) and to investigate the benefits of feedbackharnessing the fundamental asymmetry of relaxation-dominated error in theconstituent transmons. A lower-order approximate calculation extends thesepredictions to the distance-$5$ Surface-49. These results clearly indicateerror rates below the fault-tolerance threshold of surface code, and thepotential for Surface-17 to perform beyond the break-even point of quantummemory. At state-of-the-art qubit relaxation times and readout speeds,Surface-49 could surpass the break-even point of computation.

Density-matrix simulation of small surface codes under current and projected experimental noise