Non-Markovian dynamics of a driven qubit interacting with a structured environment

A qubit in a fault tolerant quantum computing architecture couples to a structured environment. This necessitates going beyond the Markovian approximation and studying the non-Markovian dynamics of a driven qubit, since the drive is required for implementing gates. In this work we theoretically study a qubit interacting with a set of discrete bosonic modes using coherent state path integrals, leading to a representation in terms of Feynman diagrams. We formulate an iterative and, in principle, scalable approach which systematically includes corrections to the propagator's poles from higher order diagrams. We study the renormalisation strength of the qubit frequency due to non-Markovian noise and discuss the consequences for the scalability of quantum computers. Further, we calculate the amplitudes for multi-photon scattering for several distributions of bosonic modes. This enables us to investigate the modifications to the memory kernel of the qubit dynamics which arise due to higher-order environmental correlators.