Quantum Error Correction in the Surface Code (Part III): Realistic Simulation of the Experimental Code Performance

The surface code is a prominent candidate for the realization of quantum error correction with superconducting qubits due to its suitable 2D-grid qubit-arrangement and its relatively high error tolerance. To guide efforts in improving the code ability to preserve logical states, it is necessary to perform realistic modeling of the system based on experimentally informative device characteristics such as individual qubit coherence times, cross-Kerr interactions, and gate fidelities. Here, we solve the complete time-evolution of a 17-qubit device implementing a distance-3 surface code using a Monte Carlo wave function approach. We also implement an effective model that captures all the desired dynamics while significantly reducing the computational requirements. Using this approach, we analyze the expected code performance as a function of experimentally relevant qubit parameters and their non-uniform distribution on the device. We also investigate the optimal parameter improvements needed to enhance logical state preservation and to reach the threshold.