Simulating a transmon implementation of the surface code, Part I

Current experimental efforts aim to realize Surface-17, a distance-3 surface-code logical qubit, using transmon qubits in a circuit QED architecture. Following experimental proposals for this device, and currently achieved fidelities on physical qubits, we define a detailed error model that takes experimentally relevant error sources into account, such as amplitude and phase damping, imperfect gate pulses, and coherent errors due to low-frequency flux noise. Using the GPU-accelerated software package ‘quantumsim’, we simulate the density matrix evolution of the logical qubit under this error model. Combining the simulation results with a minimum-weight matching decoder, we obtain predictions for the error rate of the resulting logical qubit when used as a quantum memory, and estimate the contribution of different error sources to the logical error budget.