Multi-Axis Control of a Qubit in the Presence of Unknown Non-Markovian Quantum Noise

In this paper, we consider the problem of open-loop control of a qubit that is coupled to an unknown fully quantum non-Markovian noise (either bosonic or fermionic). A graybox model that is empirically obtained from measurement data is employed to approximately represent the unknown quantum noise. The estimated model is then used to calculate the open-loop control pulses under constraints on the pulse amplitude and timing. For the control pulse optimization, we explore the use of gradient descent and genetic optimization methods. We consider the effect of finite sampling on estimating expectation values of observables and show results for single- and multi-axis control of a qubit.