Learning Single Qubit Gate Dynamics in Noisy Environments

Fault-tolerant quantum computing requires extremely precise knowledge and control of qubit dynamics during the application of a gate. Most existing quantum characterization protocols do not reveal the dynamics of a qubit during the application of a gate. We develop a data-driven learning protocol for quantum gates that builds off previous work on learning the Nakajima Mori Zwanzig formulation of open system dynamics from time series data, which allows for interpretation of the learned operators and comparison to expected dynamics. We show this learning technique can be applied to open quantum systems to learn the dynamics of a single-qubit quantum gate from simulation and experimental data. We focus on learning the Markov transition matrix, which captures the Markovian dynamics of our system, and the memory kernel, which indicates how far back in time we must look to be able to accurately predict future dynamics. We demonstrate this learning technique on two different systems: a simulation of a driven qubit coupled to stochastic noise produced by an Ornstein-Uhlenbeck process, and trapped-ion experimental data of a driven qubit coupled to an environment whose noise is not characterized ahead of time.