System-Environment Correlations in Qubit Initialization and Control

We employ numerically exact methods to study a qubit coupled to a quantum-mechanical bath, focusing on important correlation effects such as the Lamb shift and entanglement that are typically neglected in the modeling of contemporary quantum computers. We find a fundamental trade-off between speed and accuracy in qubit initialization which is important in the optimization of future reset protocols. Namely, we show analytically that at low temperatures, the deviation from the bare qubit ground state is proportional to the qubit decay rate, caused by the unavoidable entanglement between the qubit and the bath. We also find that the qubit decay is superexponential at short time scales, contrary to the result from standard Markovian approaches. However, the fidelities of quantum logic gates can be sufficiently accurately predicted by the Markovian methods. Our results can be used to develop quantum devices with engineered environments and to guide future experiments in probing the properties of the reservoirs.