Tomographic construction and prediction of superconducting qubit dynamics using the post-Markovian master equation*

Non-Markovian noise presents a particularly relevant challenge in understanding and combating decoherence in quantum computers. Using tomographic constructed state dynamics of a superconducting qubit system, we show that we can construct a phenomenological dynamical model using the post-Markovian master equation (PMME). We experimentally test our protocol to characterize the free evolution of a single qubit in one of IBMQ's cloud-based quantum processors. The resultant PMME model characterizes the cross-talk effect due to the neighboring qubits, the timescales of the qubit decoherence and dissipation process, and quantifies the degree of non-Markovianity of the system. We also demonstrate that the constructed PMME model can predict future qubit dynamics for an arbitrary single-qubit state better than the standard Lindblad model. Our model construction protocol requires sampling the qubit evolution at multiple time points for only one qubit initial state; thus, it requires less data than the process tomography and machine learning methods. The PMME has a closed-form analytical solution, making it straightforward to find the best-fit PMME model parameters via the maximum likelihood estimation method. Our protocol provides a robust estimation method for a continuous dynamical model beyond the commonly assumed Markovian approximation, leading to more accurate modeling of noisy intermediate-scale quantum (NISQ) devices.