System-environment correlations in qubit initialization and control

The impressive progress in fabricating and controlling superconducting devices for quantum information processing has reached a level where reliable theoretical predictions need to account for quantum correlations that are not captured by the conventional modeling of contemporary quantum computers. This applies particularly to the qubit initialization as the process which crucially limits typical operation times. Here, we employ numerically exact methods to study realistic implementations of a transmon qubit embedded in electromagnetic environments focusing on the most important system-reservoir correlation effects such as the Lamb shift and entanglement. For the qubit initialization we find a fundamental trade-off between speed and accuracy which sets intrinsic constraints in the optimization of future reset protocols. Instead, the fidelities of quantum logic gates can be sufficiently accurately predicted by standard treatments. Our results can be used to accurately predict the performance of specific setups and also to guide future experiments in probing low-temperature properties of qubit reservoirs.