Generalization of the linked cluster expansion computational method for arbitrary pulse sequences

Solid-state electron-spin qubits suffer from dipolar interactions with their nuclear spin baths. The nuclear spin bath causes decoherence, but it can also serve as a resource of individually addressable nuclear-spin qubits that can be harnessed for quantum computational power. Since the bath is a large, open quantum system, the dynamical processes taking place within the bath and with the electron-spin qubits are challenging to simulate for general Hamiltonians and control sequences. We present a diagrammatic computational approach to evaluate the central electronic spin problem in the presence of non-Markovian bath dynamics for arbitrary electron spin control sequences. This approach lays the groundwork for new computational capabilities, including tracking various flip-flop processes and designing multiple-pulse dynamical control sequences that display the signature of those processes.We aim to use this computational framework to explore quantum dynamics in open quantum systems.