Modeling of environmental noise in transmon qubit using dynamical decoupling

Tackling decoherence is one of the core challenges in the field of quantum computing. For superconducting qubits, coupling to the environment results in several noise channels. A rigorous characterization of the open system dynamics at the circuit Hamiltonian level is essential for a better understanding of these noise processes. Here we model the open quantum system effects for a qubit derived from a transmon circuit Hamiltonian. We use the Redfield master equation with a hybrid bath consisting of both high and low frequency components to model the effects of environment. We develop a fitting procedure using dynamical decoupling to learn the behavior of noise and use it to reproduce the experiments on processors available through IBM Quantum Experience. We test our model with quantum state fidelity experiments for random initial states. We further reproduce the effects of applied time-dependent dynamical decoupling pulses. Our model predicts all the experimental results with an average relative error of less than 1%.